{"level":"info","input":{"Message":"สวัสดีครับ คุณครูอยอแมน อิ๋ véritable นะครับ\r\nวันนี้เราจะมาเรียนโบริเศนออนไลน์เรื่องเลขยกกำลังนะครับ\r\nซึ่งเป็นตอนที่ 1 นะครับ\r\nเนื้อหาจะอยู่ในชั้นประเทศอุตสาหร่างปีที่ 5 นะครับ\r\nเรามารู้กันเลยว่า rzecz หามีอะไรบ้าง\r\nแล้วก็เราเรียนแล้วเนี่ย เราจะรู้อะไรได้บ้างนะครับ\r\nไป\r\nไปกันเลย\r\nวัตถุประสงค์ในการเรียนในวันนี้นะครับ\r\nอืม เรามีทั้งหมด 2 ข้อนะ\r\nก็คือทบทวนบริยาม และก็ทบทวนทฤษฎีบทนะครับ\r\nเกี่ยวกับเลขยกกำลังที่มีเลขชื่อกำลังเป็นจำนวนเต็มนะครับ\r\nเพราะฉะนั้น นี่คือวัตถุประสงค์ของการเรียนในคลิปนี้นะครับ\r\nนักเรียนก็ไปดูว่า เนื้อหาที่เราเรียนเนี่ย\r\nจะเป็นอย่างไรบ้างนะครับ\r\nบทนิยามที่ 1 ของเลขยกกำลังนะครับ\r\nให้ a เป็นจำนวนจริง และ n เป็นจำนวนเต็มบวก\r\na ยกกำลัง n หรือ a กำลัง n\r\nคือเราสามารถอ่านได้ทั้ง 2 แบบนะครับ\r\nก็คืออ่านว่า a ยกกำลัง n หรือ\r\na กำลัง n อันทั้ง 2 แบบเลยนะครับ\r\nเขียนแทนด้วย a กำลัง n นะครับ แล้วก็จะมีความหมายอย่างนี้นะ\r\nสำหรับตัวนี้ ก็คือ a กำลัง n ความหมายของเราก็คือ\r\na คูณ a คูณ a คูณไปเรื่อย ๆ นะครับ\r\nคุณไปถึงไหนล่ะ เท่ากับจำนวน n ตัว เท่ากับตัว n ตรงนี้นะครับ\r\nเท่ากับจุดมนต์ตรงนี้นะ เพราะฉะนั้นนะครับ\r\nเราจะเรียก a กับ n นี้นะครับ เรียกทั้งก้อนนี้เลยนะว่าเป็นเลขยกกำลังนะครับ\r\nเราก็จะเรียก a ว่าเป็นฐานของเลขยกกำลัง แล้วก็เราจะเรียก n ว่าเป็นเลขชีกกำลังนะครับ\r\nต่อไปเรียกคูป\r\nคุณครูอาจจะบอกว่าตัว a นี่คือเป็นฐานของเลขยกกำลัง\r\nและก็จะบอกว่า a นี่ก็คือเป็นเลขยกกำลังของเขานะครับ\r\nนี่ยามต่อมามีไหม\r\na กำลัง 0 เท่ากับ 1 นะครับ\r\nแต่ว่ามีเงื่อนไขปุ่มเข้ามาอีกนิดหนึ่งนะครับ\r\nก็คือ a นี่ไม่เท่ากับ 0 นะครับ\r\nบางคนก็จะพูดแบบ\r\nไปเลยว่า a ยกกำลัง 0 เท่ากับ 1\r\na เป็นอะไรก็ได้ จริง ๆ เป็นอะไรก็ได้ ไม่ถูกต้องนะครับ\r\na ของเราจะต้องไม่เท่ากับ 0 ด้วยนะครับ\r\nอันต่อมาก็คือ a\r\nยกกำลังลบ n นะครับจะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n นะครับเมื่อ a ไม่เท่ากับ 0 นะครับนิยามทั้ง 2 ตัวนี้จะมีเงื่อนไขเหมือนกันก็คือ a ไม่เท่ากับ 0 นะครับนักเรียนต้องระวังด้วยสำหรับข้อนี้นะครับเรามาดูต่อไปเรามาดูตัว\r\nว่า...\r\nทฤษฎีที่มันเกี่ยนเรื่องกับนิยามบ้างว่าเป็นยังไงบ้างนะครับ\r\nเราไปกันเลย\r\nทฤษฎีบทที่ 1 เลย\r\nเขาว่าให้ a, b เป็นจำนวนจริงที่ไม่เป็น 0\r\nและ m, n เป็นจำนวนเต็ม\r\nเราจะได้ว่านะครับ\r\nข้อ 1 เลย\r\na ยกกำลัง m คูณกับ a\r\nยกกำลัง n เท่ากับ a ยกกำลัง m บวก n นะครับ\r\nสำหรับตัวนี้นะที่สดีบทที่ 1 เนี่ย\r\nข้อที่ 1 นะครับของเรา\r\nถ้า a นะครับ ตัวนี้คือเลขชีกกำลังของเขา\r\nและก็ a ตัวนี้เลขยกกำลังเขาคือตัว n นะครับ\r\nถ้า 2 ตัวนี้เราคูณกันนะครับ\r\nเราจะเอาเลขยกกำลังของเขามาบวกกันนะครับ\r\nหรือเรียกง่าย ๆ ก็คือเราเอาทั้ง 2 ตัวนี้มาดำเนินกันโดยการบวกนะครับ\r\nนี่คือข้อแรก\r\nข้อที่ 2 เป็นอย่างไรบ้าง\r\na ยกกำลัง m\r\nทั้งหมดยกกำลัง n จะเท่ากับ a ยกกำลัง m คูณ n นะครับ\r\nซึ่งถ้าเรามีเลขยกกำลังนะครับ ที่มีเลขชิ้นกำลังตรงนี้ซ้อมกันอยู่นะครับ\r\nวิธีการของเราก็คือ\r\nให้เรานำเลขชีกกำลังมาคูณกัน\r\nก็คือเอา m กับ n มาคูณกันและเอกนะครับ\r\nอันนี้คือข้อที่ 2 สuters ที่สดีบบที่ 1 นะครับ\r\nมาดูข้อที่ 3 กัน\r\nข้อที่ 3a คูณ b ทั้งหมดยกกำลัง n นะครับ\r\nเราจะได้ว่า\r\na ยกกำลัง n คูณกับ b ยกกำลัง n\r\nเราจะสังเกตเห็นว่านะครับ\r\na กับ b ตัวนี้เนี่ย เป็นฐานของเลขยกกำลัง\r\nส่วน n ก็คือจะเป็นเลขชีกกำลังของเขานะครับ\r\nเสร็จแล้ว a กับ b เนี่ย เขาคูณกันอยู่นะครับ\r\nดังนั้นเราจึงกระจายเลขชีกกำลังนะครับ\r\nเข้าไปก็จะได้เป็น a ยกกำลัง n คูณกับ b ยกกำลัง n\r\nแต่มีข้อควรระวังนิดหนึ่งนะ ถ้าตัวนี้เป็นเครื่องหมายบกลบนี่\r\nเราจะไม่กระถับแบบนี้ไปดังขาดนะครับ\r\nเพราะว่าไม่ใช่ทฤษฎีบทที่ 1 ของเลขยกกำลังของเรานะครับ\r\nข้อ 4\r\na ส่วน b ทั้งหมดยกกำลัง n นะครับ\r\nเราจะเห็นว่าเลขชิ้นกำลังของทั้ง a และ b นี่\r\nที่เขาสวดกันอยู่ในคือกำลัง n นะครับ\r\nเราก็สามารถทำได้คล้าย ๆ กับข้อที่ 3 นะครับ\r\nแต่ข้อที่ 3 นี่เขาเป็นเครื่องหมายคูณ\r\nแต่ข้อ 4 นี่เป็นเครื่องหมายหานะครับ\r\nหรือเป็นเสร็จส่วนนั่นเองนะครับ\r\nเราก็จะได้ว่า\r\na ยกกำลัง n หารด้วย b ยกกำลัง n\r\nอันนี้คือ เป็นข้อที่ 4 ของทฤษฎีบทที่ 1 ของเรา\r\nส่วนข้อสุดท้ายคือ ข้อที่ 5 ก็คือ\r\na ยกกำลัง m ส่วนด้วย a ยกกำลัง n\r\nเราก็จะได้ว่า\r\na ยกกำลัง m ลบ n นะครับ\r\nตัวนี้มันเกิดมาจากนิยามของ\r\nนิยามที่ 1 ของเลขยกกำลังด้วยนะครับ\r\nก็คือเขาบอกว่า a ยกกำลังลบ n นะครับ\r\nจะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n\r\nอันนี้เราก็ใช้ตัวบทนิยามเข้ามาช่วยด้วย\r\nเพื่อจะได้ทฤษฎีบทที่ 1 ของข้อ 5 นักเอกนะครับนักเรียน\r\nทฤษฎีบทที่ 1 ทั้ง 5 ข้อนี้นะครับ\r\nครูจะไม่พิสูจน์ให้นักเรียนได้ดูนะ เพราะว่า\r\nคลิปนี้เป็นคลิปสำหรับการทบทวนนะครับ\r\nเพราะฉะนั้นครูขอไปที่ตัวอย่างเลยแล้วกัน\r\nตัวอย่างแรกของเรามาแล้วนะครับ\r\nโจทย์บอกว่า จงเขียน 8 กำลัง 6 คูณ 4 กำลัง 5\r\nให้อยู่ในรูปอย่างง่ายนะครับ\r\nและเลขยกกำลังทุกจำนวนมีเลขชี้กำลัง\r\nเป็นจำนวนเต็มบวกนะครับ\r\nอันนี้คือสิ่งที่โจทย์กำลังถามออกมาอยู่นะครับ\r\nเพราะฉะนั้นเนี่ย เราก็ต้องมาลองคิดด้วยวิเคราะห์ญิตนิดหนึ่ง denken yet\r\nว่าจากตัวนิยามในพฤษฎีเนี่ย\r\nเราจะสามารถนำอะไรมาใช้ได้บ้างนะครับ\r\nมาดูที่ 8 ก่อนนะครับ\r\n8 เราเรียกว่าฐานเนาะ\r\nส่วน 6 เราเรียกว่าเลขชีกำหลังของเขานะครับ\r\nส่วนนี้ 4 ก็คือเป็นฐาน ส่วน 5 ก็คือเป็นเลขยกกำลังเขานะครับ\r\nสิ่งที่เราจะสามารถนำเลขยกกำลังนี่มาดำเนินการไว้ว่าจะเป็นบวกหรือลบเนี่ย\r\nตัวฐานของเขาต้องเท่ากันก่อนครับ แล้วก็มาลองคิดดูสิครับว่า\r\nเอ๊ะ เราจะทำยังไงได้บ้างเนาะ\r\nนักเรียนในหลายคนเนี่ย ถ้านักเรียนคิดว่า\r\nจะลองคิดเองก่อนนะครับ นักเรียนก็ให้หยุดตัวคลิปของคุณครูไว้\r\nแล้วก็ลองทำก่อน แล้วก็ลองมาดูเฉลยของคุณครูด้วย\r\nตามไปด้วยก็ได้นะครับ มันเป็นการฝึกให้นักเรียนได้คิดด้วยนะครับ\r\nเพราะว่าถ้าดูตามคลิปครูไปเรื่อย ๆ บางทีทำให้เราไม่ได้คิดด้วย\r\nอ่ะ มาต่อกันเลยกันเนอะ\r\nในตัว 8 เราลองคิดดูซึ่งครับว่า 8 นี่มีอะไรเป็นตัวประกอบเนาะ\r\nมันแยกตัวประกอบได้อย่างไรนะ แล้ว C ล่ะ มีตัวประกอบอะไรบ้างนะ\r\n8 ก็คืออะไรนะ 2 คูณ 2 คูณ 2\r\nหรือเราเรียกว่าเป็น 2 กำลัง 3 นั่นเอง\r\nส่วนเลข 4 คืออะไรล่ะ 4 ก็คือ 2 คูณ 2 นะครับ\r\n2 คูณ 2 ได้ 4 ดังนั้นแสดงว่าเราก็สามารถทำเป็นเลขยกกำลังมาได้\r\nแบบนี้นั่นเอง ก็คือ 8 เมื่อกี้ที่คุณครูบอก 2 กำลัง 3 ใช่ไหมครับ\r\nแล้วเราก็มีกำลังสอนก็คือเลขชื่อกำลังตัวนี้ของเราก็คือ 6 นะ\r\n2 ยกกำลัง 3 ตัว 3 ก็คือเป็นเลขชื่อกำลัง 6 ก็เป็นเลขชื่อกำลังนะครับ\r\nส่วนตัวนี้ก็คือ 4 ของเราก็เปลี่ยนมาเป็น 2 ยกกำลัง 2 ทั้งหมดยกกำลัง 5\r\nเราจะสังเกตเห็นว่าทั้ง 2 ตัวนี้นะครับ\r\nมีเลขยกกำลังที่ซ้อนกันอยู่นะครับ\r\nจากทฤษฎีของเราก็จะได้ว่า ให้นำเลขยกกำลังนี้มาคูณกันนะครับ\r\nตัวนี้ก็เอาเลขยกกำลังคูณกันเช่นเดียวกัน\r\nเราจึงได้ตัวนี้ออกมานะครับ\r\nเป็น 2 กำลัง 18 นะครับ ก็คือเกิดมาจาก\r\n3 คูณ 6 นั่นเอง ส่วน 10 ก็คือเกิดมาจาก 2 คูณ 5 นั่นเองนะครับ\r\nหลังจากนั้น เราก็นำมาพิจัยในว่า\r\nทั้ง 2 ตัวนี้ ทั้ง 2 พตนี้ของเรานะครับ\r\nฐานของเขาเหมือนกันไหม ซึ่งก็โชคดีนะ\r\nฐานมันเป็น 2 คนดีนะครับ\r\nพอฐานเป็น 2 แล้วเราก็\r\nเขาบอกว่าอย่างไรนะ ตามทฤษฎีเรา\r\nอืม ให้นำเลขยกกำลังมาบวกกันนั่นเองนะครับ นักเรียน\r\nเพราะฉะนั้นครู ๆ ก็จะได้เป็น 2 ยกกำลัง 18 บวก 10 นะครับ\r\nก็จะได้เป็น 2 ยกกำลัง 28 นะครับ\r\nแต่ยังตอน\r\nโดดบอกอะไรเราบ้าง โดดบอกว่าให้อยู่ในรูปอย่างง่าย\r\nรูปอย่างง่ายได้ยัง ไม่มีอะไรที่จะง่ายกว่านี้แล้วนะครับ\r\nและเลขยกกำลังทุกจำนวน มีเลขยกกำลังเป็นจำนวนเต็มบวก\r\nเออ มีจำนวนเดียวนะครับ\r\nแล้วยกกำลังเป็นจำนวนเต็มบวกไหม 28 เป็นบวกไหมครับ\r\nเป็นจำนวนเต็มบวก\r\nตรงตามที่โจทย์เขาต้องการพอดีนะครับ\r\nเพราะฉะนั้นอันนี้ก็ถือว่าเป็นรูปแบบง่าย ๆ แล้วนะครับ\r\nเดี๋ยวเราลองไปดูตัวอย่างถัดไปดูนะครับว่า\r\nจะยากหรือจะง่ายอย่างไรนะครับ\r\nเราก็ให้คิดตามคุณครูไปด้วยนะครับ รังเรียน\r\nตัวอย่างที่ 2 เรามาเรียบร้อยแล้วครับนักเรียน เป็นอย่างไรบ้าง ตัวอย่างนี้ลองดูซิ โอ้ มีความยากอยู่นิดนึง ไม่เป็นไรครับนักเรียน ไม่ต้องตกอบตกใจ ไม่ต้องวิตกกังวลอะไรทั้งนั้นครับ เห็นไหมครับตัวนี้ โจทย์ว่าอย่างไรบ้าง ลองอ่านโจทย์ต่อนะครับช้า ๆ นะครับ\r\nครับ\r\nจงเขียน 6 ส่วน 5 ทั้งหมดกำลัง 3 คูณกับ 10 ตัวลัง 5\r\nให้อยู่ในรูปอย่างง่ายและเลขยกกำลังทุกจำนวน\r\nมีเลขชี้กำลังเป็นจำนวนเป็นบวกนักเรียนลองคิดตามครูไปด้วยนะ\r\nถ้าเกิดว่านักเรียนคนไหนมีกระดาษหรือยังไงก็แล้วแต่นี่\r\nก็ให้หยิบกระดาษขึ้นมาแล้วก็หยุด\r\nคลิปของครูไว้ก็ได้ แล้วก็ลองทำดูก่อนนะครับว่ามันเป็นยังไงบ้าง\r\nถ้าใครยังทำไม่ได้ครูจะไกลให้นิดนึงนะ เรามาลองดูครับ\r\n6 นี่คืออะไรครับ 6 นี่มีอะไรเป็นตัวประกอบบ้าง\r\nก็คือ 3 กับ 2 นี่ 3 คูณ 2 ได้เท่าไรนะ ได้ 6\r\nหรือบางคนว่า คุณครูผมไม่เอา 3 คูณ 2 ได้ไหม เอา 2 คูณ 3\r\nได้ครับ เพราะว่าเรามีอะไรนะ เรามี\r\nสมบัติการสำหรับพี่สำหรับการคูณด้วยนะครับ\r\nเพราะฉะนั้น 6 ของเราจะเอาเป็น 3 พูด 2 หรือ 2 พูด 3\r\nอ่า แล้วแต่นักเรียนเลยครับ ไม่มีปัญหาอะไรอยู่แล้วนะครับ\r\nอ่า สูตรเลข 10 ดูสิครับว่าเลข 10 ของเรานี่\r\nถ้าเราจะแยกตัวประกอบนี่ได้อะไรบ้าง\r\nเอ๊ ได้เลยน่ะ อ๋อ\r\nก็คือ 2 × 5 นะครับ\r\nหรือนักเรียนจะบอกว่า 5 × 2 นั่น\r\nโอ้ ตามสบายนะครับนักเรียน\r\nจะเป็น 5 × 2 3 × 2 × 5 ได้หมดครับ\r\nเพราะเรามีสมบัติของการสำหรับพี่\r\nสำหรับการคลุมนะครับ\r\nเพราะฉะนั้นเนี่ย ครูก็จะ\r\nตาม 2 ตัวนี้ได้ตามอันทันนี้นะครับ\r\n6 ของเราเมื่อกี้ก็คือบอกว่าอะไรนะ 3 คูณ 2 ส่วน 5\r\nทั้งหมดยกกำลัง 3\r\nตัวนี้นะครับ ข้อนี้ดีอย่างหนึ่งคือเราสามารถใช้ทฤษฎีหลายทฤษฎีได้นะครับ\r\nที่ของเราเนี่ย\r\nไม่ว่าจะเป็นทฤษฎีที่คูณกันแล้วสามารถกระจายเลขยกกำลังเข้าไป\r\nแล้วก็ตัวฐานข้างเดียวสามารถกระจายเลขยกกำลัง\r\nเลขชิ้นกำลังของเขาเข้าไปนะ\r\nบางครั้งนี่ครูอาจจะพูดแบบเร็วไปนิดหนึ่งนะ\r\nตัวนี้บอกว่าเป็นเลขยกกำลัง\r\nแต่ความหมายของเลขยกกำลังจริง ๆ แล้วนี่คือมันทั้งก้อนเลยนะครับ\r\nทั้งก้อนนี้เลยนะ\r\nทั้งข้อนนี้เราเรียกว่าเลขยกกำลัง ส่วนตัวนี้เป็นฐานของเขา\r\nส่วนตัวนี้เรียกว่าเลขยกกำลัง บางทีครูก็เผลอนะครับ\r\nมีบ้างเหมือนกัน บอกว่า 3 เป็นเลขยกกำลังอะไรอย่างนี้\r\nจริง ๆ แล้วคำว่าเลขยกกำลังของเรา ถือทั้งข้อนี้นะครับ\r\nตัวนี้เขาเรียกว่าเป็น\r\nเป็นฐาน ส่วน 1 ตัวนี้เรียกว่าเป็นเลขยกกำลัง\r\nถ้าตรงส่วนไหนที่ครู ๆ พูดผิดไปก็ต้องขออภัยนิดนึง\r\nเพราะว่าพูดเร็วมากนะครับในส่วนนี้\r\nโอเค เรามาต่อกันเลยแล้วกัน\r\nตัวนี้ของเรานะครับ เราจะสังเกตว่ามันมีหลาย ๆ ตัวนี้ใกล้เคียงกันแล้วนะครับ\r\nเราก็จะได้อะไรนะ\r\nกระจายเลขยกกำลังเข้าไปนะ ตัวนี้ก็กระจายได้นะ\r\nเพราะว่าตัวนี้คือหมายคูณเหมือนกัน เราจะได้ตัวนี้ออกมา\r\n3 ยกกำลัง 3 คูณ 2 กำลัง 3 หารด้วย 5 กำลัง 3\r\nตามมุมเล็บนี้เลยนะครับ ส่วนตัวนี้นะครับ\r\nคูณกับ 2 กำลัง 5 คูณกับ\r\n5 กำลัง 5 นะครับ จากวงลิฟต์นี้ด้วย\r\nสิ่งที่ตามมาเรามาดูก่อนว่า ตัวไหนที่มีฐานเหมือนกันบ้าง\r\nนี่ไงครับ 2 กำลัง 3 กับ 2 กำลัง 5\r\nมีฐานเหมือนกัน แล้วยังไงต่อครับ\r\nเขาคูณกันครับ\r\nเขาคูณกัน เขาไม่ได้หารกัน\r\nแล้วมีอีกไหม มีอีกไหม\r\nมีครับ มีอย่างไรครับ มี 5 นี่ไง มีอีก\r\nเพราะฉะนั้นตัวนี้เป็นอย่างไรบ้างครับ\r\nตัวนี้\r\nเขาหารกันครับ เขาหาร เขาไม่ได้คูณ\r\nเพราะฉะนั้นถ้าหารกันทำอย่างไรนะ\r\nให้เราดำเนินการโดยนำเลขชิ้นกำลังมามาลบกันใช่ไหมครับ\r\nถ้าเราเอา 5 กำลัง 3 นี่ ขึ้นไปคูณกับตัวนี้นะครับ\r\nมันก็จะได้เป็น 5 เยอะกำลัง 5 ลบ 3 นะครับ\r\nส่วนตัวนี้เนี่ย ก็คือเอามาบวกกันอยู่แล้ว เพราะว่าเขาคูณกัน\r\nเราจะได้ตัวนี้ออกมานะ เป็น 3 กำลัง 3 ตัวนี้เนี่ย ไม่ต้องไปยุกอะไรกับเขา\r\nเพราะว่าไม่มีตัวไหนที่มีฐานเหมือนกันเลย ส่วนตัวนี้ก็คือ 2 กำลัง 3\r\n3 ตัวนี้นะ แล้วก็บวกกับ 5 คือตัวนี้นะครับ\r\nตัวนี้นะครับ คูณกับ 5 กำลังลบ 3 ใช่ไหม\r\nถ้าเราย้ายขึ้นไปคูณนะ กูขออนุญาตใช้คำนี้ด้วยกัน\r\nเพราะว่าจริง ๆ แล้วใช้คำว่าย้ายขึ้นไปคูณ มันไม่ใช่นะครับ\r\nก็คือมันคุ้นด้วยตัวอินเวิร์ตของเขานั่นเองนะครับ\r\nก็จะได้เป็น\r\n5 เยอะกำลัง 5 รูป 3 นะครับ\r\nสุดท้ายจริง ๆ เราก็จะได้อะไรบ้าง\r\n3 กำลัง 3 คูณ 2 กำลัง 8\r\nคูณ 5 กำลัง 2 นะครับ\r\nตรงตามสิ่งที่โจทย์ต้องการหรือยัง เดี๋ยวเราว่าอะไรบ้าง\r\nให้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกตัวมีเลขชิกกำลังเป็นจำนวนเต็มบวกมีหลายตัวนะ เมื่อกี้เรามี 2 ตัวเดียวใช่ไหม\r\nข้ออธิบาลมาตัวนี้เรามี มีทั้ง 3 มีทั้ง 2 มีทั้ง 5\r\nแล้วเลขชิกกำลังเขาเนี่ย เป็นจำนวนเต็มบวกหรือยัง\r\nหรือยังครับ เป็นเรียบร้อยแล้วนะครับ\r\nเพราะฉะนั้นข้อนี้เนี่ย เราก็\r\nครูbedit ที่ 9 นิดนึงเหล่าความใจ ہوมาว่า นายคงได้จับคำนึงจุดนงค่ะ\r\nเพื่อนลูกคุม beberodenสั่นที่ 5-U\r\n expedit นับประสีทั้งโภกตรด governance\r\nyo doot doot doot\r\ncokor doot\r\nc sixty doot\r\ncokor doot doot\r\ncokor doot doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\nดูนะครับว่ามันจะเป็นอย่างไรบ้าง\r\nสำหรับตัวอย่างนี้ของเรานะครับ\r\nก็จะมีความแตกต่างจากตัวอย่าง\r\n2 ตัวอย่างที่เราทำผ่านมานะครับ\r\nแต่ไอ้ไงก็คือตัวนี้นะครับ\r\nเป็นตัวแปรนะครับ\r\nไม่ใช่ตัวจำนวนเหมือนที่ผ่านมานะครับ\r\nจดข้อนี้บอกว่าอย่างไรบ้าง\r\nให้ x, y และ measure จูดจริงที่ไม่เป็น 0 นะครับ\r\nจงทำให้พ Matth ต่อไปนี้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกจำนวนมีเลขชื่อกำลังเป็นจำนวนเต็มบวก นะครับ\r\nอันนี้คือสิ่งที่โจทย์กำลังถามเรารู้ไหม\r\nอยู่ตรงนี้ครับดังเรียน\r\nx ส่วน y ทั้งหมดกำลัง 3\r\nคูณอยู่กับ y กำลัง 2 x ส่วนด้วย z นะครับ\r\nตัวนี้ไม่มีเลขยกกำลังมาสอนตรงนี้นะ\r\nแต่ตัวนี้มีนะครับ ก็คือยกกำลัง 3 นะครับ\r\nเพราะฉะนั้นวิธีการของเราก็คือเราก็ทำเหมือนกับจำนวนนะครับ\r\nที่เป็นตัวเลขนะ เหมือนปกติเลยก็คือการใจ\r\nเลขชื่อกำลังเข้าไปนะครับ เราก็จะได้ออกมาเป็นดังนี้นะครับ\r\nเป็น x กำลัง 3 ส่วน y กำลัง 3 นะครับ ตามมุมเล็บแรกของเราเลยนะ\r\nส่วนตัวนี้นะครับ เราก็สามารถเอามุมเล็บออกได้นะ\r\nเพราะว่าเป็นเครื่องหมายคูณนะครับ เราไม่ต้องมาใส่เครื่องหมายคูณเข้าไปนะครับ\r\nถ้าเป็นตัวแปลกแบบนี้ก็คือเป็น y กำลัง 2x ส่วนด้วย\r\nz นะตัววงเล็บที่ 2 เรากระจายมาซึ่ง z ก็จะเป็นคูณกับ y กันอัน 3 จากวงเล็บแรกนั่นเองนะครับ\r\nอันดับต่อมานะครับนักเรียนลองคิดตามครูนะว่าสิ่งที่เราต้องการทำนี่เพื่ออะไรบ้าง\r\nยังไม่ไหมที่ครูเคยบอกก็คืออะไร\r\nให้ไปดูว่าฐานของเลขยกกำลังในแต่ละตัวน่ะ มีตัวไหนที่เขาเหมือนกันไหมนะครับ\r\nที่มีค่าเท่ากันไหม นี่ไงครับนักเรียน x\r\nตัวนี้ x กันลัง 3 ตัวนี้ x ยกกำลังอะไร\r\nถ้าเราไม่เขียนก็คือ x ยกกำลัง 1 ครับนักเรียนนะครับ\r\nส่วน y ตัวนี้นะครับ ตัวนี้คือเป็น y กันลัง 2\r\nส่วนด้วย y กำลัง 3 นะครับ\r\nเพราะฉะนั้น 2 ตัวนี้นะครับ เขาคูณกันอยู่\r\nแต่ 2 ตัวนี้นะครับ ตัว y นี้เขาหันกันนะครับ\r\nเพราะฉะนั้นหรือ y กำลัง 2 ส่วนด้วย y กำลัง 3 นั่นเอง\r\nถ้าครูอ่านเฉพาะตัวนี้นะ เพราะฉะนั้นเราก็สามารถกระทำกับ\r\nx กลาง 3 กับ x กลาง 1 ยังไงได้บ้าง\r\nส่วนตัว y เราจะทำยังไงบ้างนะ\r\nนักเรียนลองคิดตามนะว่า คุณครูจะทำยังไงบ้าง\r\nคุณครูทำอย่างนี้ครับ ก็คือ x กำลัง 3 บวก 1\r\nส่วนตัว y นะครับ กำลัง 3 ลบ 2 ตัวนี้คือตัวส่วนนะ\r\nสังเกตเห็นไหมครับ คุณครูจะไม่เอาตัว 3 นะครับ\r\nคูณด้วย y ยกกำลังลบ 3 ตรงนี้นะ\r\nเพราะบางคนก็อาจจะเอาขึ้นไปขึ้นบนตรงนี้นะครับ\r\nเป็นลบ 3 ตรงนี้นะครับ\r\nบางทีพอทำปุ๊บเนี่ย\r\nค่าตรงนี้ไม่ได้ติดลบนะครับ\r\nมันจะกลายเป็น 2 ลบ 3 ก็คือเป็นลบ 1\r\nแต่ว่าข้อนี้เราต้องการเลขชี่กำลังเป็นจำนวนเต็มบวก\r\nดังนั้นเนี่ยคุณครูทำครั้งเดียวไปเลย\r\nก็คือเอา 2 ตรงนี้นะครับ\r\nมาดำเดือนกันก็คือ รบกับ 3 ตรงนี้\r\nเราก็จะได้เป็น y กำลัง 3 รบ 2 นะคะ даже grad\r\nเพราะฉะนั้นนี่ คือนักเรียนต่างคนไม่ถนัด\r\nก็คือถนัดที่จะเอาไปอยู่ข้างบนอย่างเดียวนะ\r\nอย่างนี้ก็ได้นะครับ\r\nไม่ผิดแต่อย่างไร\r\nแต่สุดท้าย อย่าลืมนะ ว่าเลขชีพกำลังของเราทุกตัวนะครับ\r\nจะต้องเป็นเป็นบวกหมดเลย\r\nตรงนี้เราก็จะได้เป็น x กระดัง 4 ส่วนด้วย yz นะครับนักเรียน\r\nเป็นอย่างไรบ้าง เราดูตัวอย่างนะครับ\r\nมาทั้ง 3 มาแล้ว ทั้งตัวอย่างที่เป็นจำนวดที่เป็นตัวเลข\r\nกับตัวอย่างที่เป็นตัวแปรนะครับ เพราะฉะนั้นนี่\r\nนักเรียนไม่ต้องพร้อมคุณอะไรนะครับ\r\nค่อย ๆ ทำไปนะครับ\r\nแล้วก็ค่อย ๆ ดูว่าทฤษฎีอะไรที่เราสามารถนำมาใช้ในแต่ละข้อได้บ้างนะครับ\r\nอ่ะ เรามาดูสิ่งที่เราได้เรียนรู้อะไรบ้างในบทเรียนในวันนี้นะครับ\r\nก็คือ\r\nคุณครูบอกแล้วตอนต้นคลิปนะว่า สิ่งที่เราควรจะรู้มีไหนบ้าง\r\nก็คือวันนี้เราก็จะได้มาทบทวนนะครับ บทนิยามของเขา\r\nซึ่งต้นคลิปคุณครูก็บอกไปแล้ว ก็คือเราก็รู้ว่า\r\nไอ้ตัว a กำลัง n ตรงนี้นะครับ ก็คือเป็นเลขยกกำลังนะ\r\nเรามีความหมายทางนี้ก็คือ ถ้า a กำลัง n ก็คือ a คูณกันไปทั้งหมด n ตัวนะครับ\r\nเราก็จะเรียกว่า a กำลัง n คือเลขยกกำลัง เรียก a ว่าเป็นฐานของเลขยกกำลัง\r\nแล้วก็เรียก n ว่าเป็นเลขชื่อกำลังนะครับ\r\nส่วนนิยามอีก 2 ตัวก็คือ a กำลัง 0 ได้เท่ากับ 1\r\nโดยที่ a ไม่เท่ากับ 0 นะครับ\r\nส่วนอีกอันหนึ่งก็คือ a กำลังลบ n เท่ากับ 1\r\nส่วนด้วย a กำลัง n นะครับ เมื่อ a ไม่เท่ากับ 0 นะครับ\r\nอันนี้คือสิ่งที่เราได้เรียนในวันนี้นะครับ\r\nอีกอันหนึ่งก็คือตัวทฤษฎีบทนะครับ\r\nที่เราได้ทบทวนไปตอนต้นคลิปก็คือ\r\nตัวแรกก็คือตัวนี้นะ\r\nab เป็นยกบันจริงที่ไม่ใช่ 0 แล้วก็ mn เป็นยกบันเต็มนะครับ\r\nเราก็ได้ทั้งหมด 5 ข้อก็คือ a m x a n เท่ากับ a n นะครับ\r\nแล้วก็ข้อ 2 ก็คือ a m ทั้งหมดกำลัง n เราก็จะได้ว่าเท่ากับ na a m n\r\nแล้วก็ข้อ 3 ก็คือ a คูณ b ทั้งหมดยกกำลัง n นะครับ\r\nเราก็จะได้ว่า a กำลัง n คูณกับ b กำลัง n นะครับ\r\nข้อ 4 ก็คือ a ส่วน b ทั้งหมดยกกำลัง n ก็จะเท่ากับ a กำลัง n ส่วนด้วย\r\nมีกำลัง n อันนี้นะครับที่คุณครูได้อธิบายในตรงคลิปไปแล้วแล้วก็ข้อสุดท้ายของเราก็คือ a กำลัง n ส่วนด้วย\r\na กำลัง n จะเท่ากับ a กำลัง m ลบ n นะครับ\r\nอ่า เป็นยังไงบ้างครับนักเรียนคลิปในวันนี้นะครับ\r\nแต่ว่าก่อนที่จะจบคลิปเนี่ยคุณครูอาจจะให้\r\nตัวตัวอย่างและก็แบบฝึกหัดเนี่ยเพื่อให้นักเรียนเนี่ยไปไปฝึกอีกทีนึงนะครับเดี๋ยวเราเจอกันในคลิปหน้านะครับมาดูว่าคุณครูมีอะไรจะมาให้นักเรียนได้ได้เรียนรู้นะครับบ้างนะครับวันนี้ก็ขอจบคลิปไว้เพียงเท่านี้สวัสดีครับ\r\nครับ","Candidate":3,"Ordering":true,"Spacing":true,"SpacingFile":null,"WordToNumber":true,"EnWord":true,"ThWord":true,"Transliteration":true,"TransliterationMatchingCase":"insensitive","TransliterationFile":null,"Reduplication":true,"Corrector":true,"Register":true,"RegisterFile":null},"time":"2024-09-16T17:14:02+07:00","caller":"/go/src/app/internal/handler/text_improver.go:95"}
{"level":"info","ordering":"สวัสดีครับ คุณครูอยอแมน อิ๋ véritable นะครับ\r\nวันนี้เราจะมาเรียนโบริเศนออนไลน์เรื่องเลขยกกำลังนะครับ\r\nซึ่งเป็นตอนที่ 1 นะครับ\r\nเนื้อหาจะอยู่ในชั้นประเทศอุตสาหร่างปีที่ 5 นะครับ\r\nเรามารู้กันเลยว่า rzecz หามีอะไรบ้าง\r\nแล้วก็เราเรียนแล้วเนี่ย เราจะรู้อะไรได้บ้างนะครับ\r\nไป\r\nไปกันเลย\r\nวัตถุประสงค์ในการเรียนในวันนี้นะครับ\r\nอืม เรามีทั้งหมด 2 ข้อนะ\r\nก็คือทบทวนบริยาม และก็ทบทวนทฤษฎีบทนะครับ\r\nเกี่ยวกับเลขยกกำลังที่มีเลขชื่อกำลังเป็นจำนวนเต็มนะครับ\r\nเพราะฉะนั้น นี่คือวัตถุประสงค์ของการเรียนในคลิปนี้นะครับ\r\nนักเรียนก็ไปดูว่า เนื้อหาที่เราเรียนเนี่ย\r\nจะเป็นอย่างไรบ้างนะครับ\r\nบทนิยามที่ 1 ของเลขยกกำลังนะครับ\r\nให้ a เป็นจำนวนจริง และ n เป็นจำนวนเต็มบวก\r\na ยกกำลัง n หรือ a กำลัง n\r\nคือเราสามารถอ่านได้ทั้ง 2 แบบนะครับ\r\nก็คืออ่านว่า a ยกกำลัง n หรือ\r\na กำลัง n อันทั้ง 2 แบบเลยนะครับ\r\nเขียนแทนด้วย a กำลัง n นะครับ แล้วก็จะมีความหมายอย่างนี้นะ\r\nสำหรับตัวนี้ ก็คือ a กำลัง n ความหมายของเราก็คือ\r\na คูณ a คูณ a คูณไปเรื่อย ๆ นะครับ\r\nคุณไปถึงไหนล่ะ เท่ากับจำนวน n ตัว เท่ากับตัว n ตรงนี้นะครับ\r\nเท่ากับจุดมนต์ตรงนี้นะ เพราะฉะนั้นนะครับ\r\nเราจะเรียก a กับ n นี้นะครับ เรียกทั้งก้อนนี้เลยนะว่าเป็นเลขยกกำลังนะครับ\r\nเราก็จะเรียก a ว่าเป็นฐานของเลขยกกำลัง แล้วก็เราจะเรียก n ว่าเป็นเลขชีกกำลังนะครับ\r\nต่อไปเรียกคูป\r\nคุณครูอาจจะบอกว่าตัว a นี่คือเป็นฐานของเลขยกกำลัง\r\nและก็จะบอกว่า a นี่ก็คือเป็นเลขยกกำลังของเขานะครับ\r\nนี่ยามต่อมามีไหม\r\na กำลัง 0 เท่ากับ 1 นะครับ\r\nแต่ว่ามีเงื่อนไขปุ่มเข้ามาอีกนิดหนึ่งนะครับ\r\nก็คือ a นี่ไม่เท่ากับ 0 นะครับ\r\nบางคนก็จะพูดแบบ\r\nไปเลยว่า a ยกกำลัง 0 เท่ากับ 1\r\na เป็นอะไรก็ได้ จริง ๆ เป็นอะไรก็ได้ ไม่ถูกต้องนะครับ\r\na ของเราจะต้องไม่เท่ากับ 0 ด้วยนะครับ\r\nอันต่อมาก็คือ a\r\nยกกำลังลบ n นะครับจะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n นะครับเมื่อ a ไม่เท่ากับ 0 นะครับนิยามทั้ง 2 ตัวนี้จะมีเงื่อนไขเหมือนกันก็คือ a ไม่เท่ากับ 0 นะครับนักเรียนต้องระวังด้วยสำหรับข้อนี้นะครับเรามาดูต่อไปเรามาดูตัว\r\nว่า...\r\nทฤษฎีที่มันเกี่ยนเรื่องกับนิยามบ้างว่าเป็นยังไงบ้างนะครับ\r\nเราไปกันเลย\r\nทฤษฎีบทที่ 1 เลย\r\nเขาว่าให้ a, b เป็นจำนวนจริงที่ไม่เป็น 0\r\nและ m, n เป็นจำนวนเต็ม\r\nเราจะได้ว่านะครับ\r\nข้อ 1 เลย\r\na ยกกำลัง m คูณกับ a\r\nยกกำลัง n เท่ากับ a ยกกำลัง m บวก n นะครับ\r\nสำหรับตัวนี้นะที่สดีบทที่ 1 เนี่ย\r\nข้อที่ 1 นะครับของเรา\r\nถ้า a นะครับ ตัวนี้คือเลขชีกกำลังของเขา\r\nและก็ a ตัวนี้เลขยกกำลังเขาคือตัว n นะครับ\r\nถ้า 2 ตัวนี้เราคูณกันนะครับ\r\nเราจะเอาเลขยกกำลังของเขามาบวกกันนะครับ\r\nหรือเรียกง่าย ๆ ก็คือเราเอาทั้ง 2 ตัวนี้มาดำเนินกันโดยการบวกนะครับ\r\nนี่คือข้อแรก\r\nข้อที่ 2 เป็นอย่างไรบ้าง\r\na ยกกำลัง m\r\nทั้งหมดยกกำลัง n จะเท่ากับ a ยกกำลัง m คูณ n นะครับ\r\nซึ่งถ้าเรามีเลขยกกำลังนะครับ ที่มีเลขชิ้นกำลังตรงนี้ซ้อมกันอยู่นะครับ\r\nวิธีการของเราก็คือ\r\nให้เรานำเลขชีกกำลังมาคูณกัน\r\nก็คือเอา m กับ n มาคูณกันและเอกนะครับ\r\nอันนี้คือข้อที่ 2 สuters ที่สดีบบที่ 1 นะครับ\r\nมาดูข้อที่ 3 กัน\r\nข้อที่ 3a คูณ b ทั้งหมดยกกำลัง n นะครับ\r\nเราจะได้ว่า\r\na ยกกำลัง n คูณกับ b ยกกำลัง n\r\nเราจะสังเกตเห็นว่านะครับ\r\na กับ b ตัวนี้เนี่ย เป็นฐานของเลขยกกำลัง\r\nส่วน n ก็คือจะเป็นเลขชีกกำลังของเขานะครับ\r\nเสร็จแล้ว a กับ b เนี่ย เขาคูณกันอยู่นะครับ\r\nดังนั้นเราจึงกระจายเลขชีกกำลังนะครับ\r\nเข้าไปก็จะได้เป็น a ยกกำลัง n คูณกับ b ยกกำลัง n\r\nแต่มีข้อควรระวังนิดหนึ่งนะ ถ้าตัวนี้เป็นเครื่องหมายบกลบนี่\r\nเราจะไม่กระถับแบบนี้ไปดังขาดนะครับ\r\nเพราะว่าไม่ใช่ทฤษฎีบทที่ 1 ของเลขยกกำลังของเรานะครับ\r\nข้อ 4\r\na ส่วน b ทั้งหมดยกกำลัง n นะครับ\r\nเราจะเห็นว่าเลขชิ้นกำลังของทั้ง a และ b นี่\r\nที่เขาสวดกันอยู่ในคือกำลัง n นะครับ\r\nเราก็สามารถทำได้คล้าย ๆ กับข้อที่ 3 นะครับ\r\nแต่ข้อที่ 3 นี่เขาเป็นเครื่องหมายคูณ\r\nแต่ข้อ 4 นี่เป็นเครื่องหมายหานะครับ\r\nหรือเป็นเสร็จส่วนนั่นเองนะครับ\r\nเราก็จะได้ว่า\r\na ยกกำลัง n หารด้วย b ยกกำลัง n\r\nอันนี้คือ เป็นข้อที่ 4 ของทฤษฎีบทที่ 1 ของเรา\r\nส่วนข้อสุดท้ายคือ ข้อที่ 5 ก็คือ\r\na ยกกำลัง m ส่วนด้วย a ยกกำลัง n\r\nเราก็จะได้ว่า\r\na ยกกำลัง m ลบ n นะครับ\r\nตัวนี้มันเกิดมาจากนิยามของ\r\nนิยามที่ 1 ของเลขยกกำลังด้วยนะครับ\r\nก็คือเขาบอกว่า a ยกกำลังลบ n นะครับ\r\nจะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n\r\nอันนี้เราก็ใช้ตัวบทนิยามเข้ามาช่วยด้วย\r\nเพื่อจะได้ทฤษฎีบทที่ 1 ของข้อ 5 นักเอกนะครับนักเรียน\r\nทฤษฎีบทที่ 1 ทั้ง 5 ข้อนี้นะครับ\r\nครูจะไม่พิสูจน์ให้นักเรียนได้ดูนะ เพราะว่า\r\nคลิปนี้เป็นคลิปสำหรับการทบทวนนะครับ\r\nเพราะฉะนั้นครูขอไปที่ตัวอย่างเลยแล้วกัน\r\nตัวอย่างแรกของเรามาแล้วนะครับ\r\nโจทย์บอกว่า จงเขียน 8 กำลัง 6 คูณ 4 กำลัง 5\r\nให้อยู่ในรูปอย่างง่ายนะครับ\r\nและเลขยกกำลังทุกจำนวนมีเลขชี้กำลัง\r\nเป็นจำนวนเต็มบวกนะครับ\r\nอันนี้คือสิ่งที่โจทย์กำลังถามออกมาอยู่นะครับ\r\nเพราะฉะนั้นเนี่ย เราก็ต้องมาลองคิดด้วยวิเคราะห์ญิตนิดหนึ่ง denken yet\r\nว่าจากตัวนิยามในพฤษฎีเนี่ย\r\nเราจะสามารถนำอะไรมาใช้ได้บ้างนะครับ\r\nมาดูที่ 8 ก่อนนะครับ\r\n8 เราเรียกว่าฐานเนาะ\r\nส่วน 6 เราเรียกว่าเลขชีกำหลังของเขานะครับ\r\nส่วนนี้ 4 ก็คือเป็นฐาน ส่วน 5 ก็คือเป็นเลขยกกำลังเขานะครับ\r\nสิ่งที่เราจะสามารถนำเลขยกกำลังนี่มาดำเนินการไว้ว่าจะเป็นบวกหรือลบเนี่ย\r\nตัวฐานของเขาต้องเท่ากันก่อนครับ แล้วก็มาลองคิดดูสิครับว่า\r\nเอ๊ะ เราจะทำยังไงได้บ้างเนาะ\r\nนักเรียนในหลายคนเนี่ย ถ้านักเรียนคิดว่า\r\nจะลองคิดเองก่อนนะครับ นักเรียนก็ให้หยุดตัวคลิปของคุณครูไว้\r\nแล้วก็ลองทำก่อน แล้วก็ลองมาดูเฉลยของคุณครูด้วย\r\nตามไปด้วยก็ได้นะครับ มันเป็นการฝึกให้นักเรียนได้คิดด้วยนะครับ\r\nเพราะว่าถ้าดูตามคลิปครูไปเรื่อย ๆ บางทีทำให้เราไม่ได้คิดด้วย\r\nอ่ะ มาต่อกันเลยกันเนอะ\r\nในตัว 8 เราลองคิดดูซึ่งครับว่า 8 นี่มีอะไรเป็นตัวประกอบเนาะ\r\nมันแยกตัวประกอบได้อย่างไรนะ แล้ว C ล่ะ มีตัวประกอบอะไรบ้างนะ\r\n8 ก็คืออะไรนะ 2 คูณ 2 คูณ 2\r\nหรือเราเรียกว่าเป็น 2 กำลัง 3 นั่นเอง\r\nส่วนเลข 4 คืออะไรล่ะ 4 ก็คือ 2 คูณ 2 นะครับ\r\n2 คูณ 2 ได้ 4 ดังนั้นแสดงว่าเราก็สามารถทำเป็นเลขยกกำลังมาได้\r\nแบบนี้นั่นเอง ก็คือ 8 เมื่อกี้ที่คุณครูบอก 2 กำลัง 3 ใช่ไหมครับ\r\nแล้วเราก็มีกำลังสอนก็คือเลขชื่อกำลังตัวนี้ของเราก็คือ 6 นะ\r\n2 ยกกำลัง 3 ตัว 3 ก็คือเป็นเลขชื่อกำลัง 6 ก็เป็นเลขชื่อกำลังนะครับ\r\nส่วนตัวนี้ก็คือ 4 ของเราก็เปลี่ยนมาเป็น 2 ยกกำลัง 2 ทั้งหมดยกกำลัง 5\r\nเราจะสังเกตเห็นว่าทั้ง 2 ตัวนี้นะครับ\r\nมีเลขยกกำลังที่ซ้อนกันอยู่นะครับ\r\nจากทฤษฎีของเราก็จะได้ว่า ให้นำเลขยกกำลังนี้มาคูณกันนะครับ\r\nตัวนี้ก็เอาเลขยกกำลังคูณกันเช่นเดียวกัน\r\nเราจึงได้ตัวนี้ออกมานะครับ\r\nเป็น 2 กำลัง 18 นะครับ ก็คือเกิดมาจาก\r\n3 คูณ 6 นั่นเอง ส่วน 10 ก็คือเกิดมาจาก 2 คูณ 5 นั่นเองนะครับ\r\nหลังจากนั้น เราก็นำมาพิจัยในว่า\r\nทั้ง 2 ตัวนี้ ทั้ง 2 พตนี้ของเรานะครับ\r\nฐานของเขาเหมือนกันไหม ซึ่งก็โชคดีนะ\r\nฐานมันเป็น 2 คนดีนะครับ\r\nพอฐานเป็น 2 แล้วเราก็\r\nเขาบอกว่าอย่างไรนะ ตามทฤษฎีเรา\r\nอืม ให้นำเลขยกกำลังมาบวกกันนั่นเองนะครับ นักเรียน\r\nเพราะฉะนั้นครู ๆ ก็จะได้เป็น 2 ยกกำลัง 18 บวก 10 นะครับ\r\nก็จะได้เป็น 2 ยกกำลัง 28 นะครับ\r\nแต่ยังตอน\r\nโดดบอกอะไรเราบ้าง โดดบอกว่าให้อยู่ในรูปอย่างง่าย\r\nรูปอย่างง่ายได้ยัง ไม่มีอะไรที่จะง่ายกว่านี้แล้วนะครับ\r\nและเลขยกกำลังทุกจำนวน มีเลขยกกำลังเป็นจำนวนเต็มบวก\r\nเออ มีจำนวนเดียวนะครับ\r\nแล้วยกกำลังเป็นจำนวนเต็มบวกไหม 28 เป็นบวกไหมครับ\r\nเป็นจำนวนเต็มบวก\r\nตรงตามที่โจทย์เขาต้องการพอดีนะครับ\r\nเพราะฉะนั้นอันนี้ก็ถือว่าเป็นรูปแบบง่าย ๆ แล้วนะครับ\r\nเดี๋ยวเราลองไปดูตัวอย่างถัดไปดูนะครับว่า\r\nจะยากหรือจะง่ายอย่างไรนะครับ\r\nเราก็ให้คิดตามคุณครูไปด้วยนะครับ รังเรียน\r\nตัวอย่างที่ 2 เรามาเรียบร้อยแล้วครับนักเรียน เป็นอย่างไรบ้าง ตัวอย่างนี้ลองดูซิ โอ้ มีความยากอยู่นิดนึง ไม่เป็นไรครับนักเรียน ไม่ต้องตกอบตกใจ ไม่ต้องวิตกกังวลอะไรทั้งนั้นครับ เห็นไหมครับตัวนี้ โจทย์ว่าอย่างไรบ้าง ลองอ่านโจทย์ต่อนะครับช้า ๆ นะครับ\r\nครับ\r\nจงเขียน 6 ส่วน 5 ทั้งหมดกำลัง 3 คูณกับ 10 ตัวลัง 5\r\nให้อยู่ในรูปอย่างง่ายและเลขยกกำลังทุกจำนวน\r\nมีเลขชี้กำลังเป็นจำนวนเป็นบวกนักเรียนลองคิดตามครูไปด้วยนะ\r\nถ้าเกิดว่านักเรียนคนไหนมีกระดาษหรือยังไงก็แล้วแต่นี่\r\nก็ให้หยิบกระดาษขึ้นมาแล้วก็หยุด\r\nคลิปของครูไว้ก็ได้ แล้วก็ลองทำดูก่อนนะครับว่ามันเป็นยังไงบ้าง\r\nถ้าใครยังทำไม่ได้ครูจะไกลให้นิดนึงนะ เรามาลองดูครับ\r\n6 นี่คืออะไรครับ 6 นี่มีอะไรเป็นตัวประกอบบ้าง\r\nก็คือ 3 กับ 2 นี่ 3 คูณ 2 ได้เท่าไรนะ ได้ 6\r\nหรือบางคนว่า คุณครูผมไม่เอา 3 คูณ 2 ได้ไหม เอา 2 คูณ 3\r\nได้ครับ เพราะว่าเรามีอะไรนะ เรามี\r\nสมบัติการสำหรับพี่สำหรับการคูณด้วยนะครับ\r\nเพราะฉะนั้น 6 ของเราจะเอาเป็น 3 พูด 2 หรือ 2 พูด 3\r\nอ่า แล้วแต่นักเรียนเลยครับ ไม่มีปัญหาอะไรอยู่แล้วนะครับ\r\nอ่า สูตรเลข 10 ดูสิครับว่าเลข 10 ของเรานี่\r\nถ้าเราจะแยกตัวประกอบนี่ได้อะไรบ้าง\r\nเอ๊ ได้เลยน่ะ อ๋อ\r\nก็คือ 2 × 5 นะครับ\r\nหรือนักเรียนจะบอกว่า 5 × 2 นั่น\r\nโอ้ ตามสบายนะครับนักเรียน\r\nจะเป็น 5 × 2 3 × 2 × 5 ได้หมดครับ\r\nเพราะเรามีสมบัติของการสำหรับพี่\r\nสำหรับการคลุมนะครับ\r\nเพราะฉะนั้นเนี่ย ครูก็จะ\r\nตาม 2 ตัวนี้ได้ตามอันทันนี้นะครับ\r\n6 ของเราเมื่อกี้ก็คือบอกว่าอะไรนะ 3 คูณ 2 ส่วน 5\r\nทั้งหมดยกกำลัง 3\r\nตัวนี้นะครับ ข้อนี้ดีอย่างหนึ่งคือเราสามารถใช้ทฤษฎีหลายทฤษฎีได้นะครับ\r\nที่ของเราเนี่ย\r\nไม่ว่าจะเป็นทฤษฎีที่คูณกันแล้วสามารถกระจายเลขยกกำลังเข้าไป\r\nแล้วก็ตัวฐานข้างเดียวสามารถกระจายเลขยกกำลัง\r\nเลขชิ้นกำลังของเขาเข้าไปนะ\r\nบางครั้งนี่ครูอาจจะพูดแบบเร็วไปนิดหนึ่งนะ\r\nตัวนี้บอกว่าเป็นเลขยกกำลัง\r\nแต่ความหมายของเลขยกกำลังจริง ๆ แล้วนี่คือมันทั้งก้อนเลยนะครับ\r\nทั้งก้อนนี้เลยนะ\r\nทั้งข้อนนี้เราเรียกว่าเลขยกกำลัง ส่วนตัวนี้เป็นฐานของเขา\r\nส่วนตัวนี้เรียกว่าเลขยกกำลัง บางทีครูก็เผลอนะครับ\r\nมีบ้างเหมือนกัน บอกว่า 3 เป็นเลขยกกำลังอะไรอย่างนี้\r\nจริง ๆ แล้วคำว่าเลขยกกำลังของเรา ถือทั้งข้อนี้นะครับ\r\nตัวนี้เขาเรียกว่าเป็น\r\nเป็นฐาน ส่วน 1 ตัวนี้เรียกว่าเป็นเลขยกกำลัง\r\nถ้าตรงส่วนไหนที่ครู ๆ พูดผิดไปก็ต้องขออภัยนิดนึง\r\nเพราะว่าพูดเร็วมากนะครับในส่วนนี้\r\nโอเค เรามาต่อกันเลยแล้วกัน\r\nตัวนี้ของเรานะครับ เราจะสังเกตว่ามันมีหลาย ๆ ตัวนี้ใกล้เคียงกันแล้วนะครับ\r\nเราก็จะได้อะไรนะ\r\nกระจายเลขยกกำลังเข้าไปนะ ตัวนี้ก็กระจายได้นะ\r\nเพราะว่าตัวนี้คือหมายคูณเหมือนกัน เราจะได้ตัวนี้ออกมา\r\n3 ยกกำลัง 3 คูณ 2 กำลัง 3 หารด้วย 5 กำลัง 3\r\nตามมุมเล็บนี้เลยนะครับ ส่วนตัวนี้นะครับ\r\nคูณกับ 2 กำลัง 5 คูณกับ\r\n5 กำลัง 5 นะครับ จากวงลิฟต์นี้ด้วย\r\nสิ่งที่ตามมาเรามาดูก่อนว่า ตัวไหนที่มีฐานเหมือนกันบ้าง\r\nนี่ไงครับ 2 กำลัง 3 กับ 2 กำลัง 5\r\nมีฐานเหมือนกัน แล้วยังไงต่อครับ\r\nเขาคูณกันครับ\r\nเขาคูณกัน เขาไม่ได้หารกัน\r\nแล้วมีอีกไหม มีอีกไหม\r\nมีครับ มีอย่างไรครับ มี 5 นี่ไง มีอีก\r\nเพราะฉะนั้นตัวนี้เป็นอย่างไรบ้างครับ\r\nตัวนี้\r\nเขาหารกันครับ เขาหาร เขาไม่ได้คูณ\r\nเพราะฉะนั้นถ้าหารกันทำอย่างไรนะ\r\nให้เราดำเนินการโดยนำเลขชิ้นกำลังมามาลบกันใช่ไหมครับ\r\nถ้าเราเอา 5 กำลัง 3 นี่ ขึ้นไปคูณกับตัวนี้นะครับ\r\nมันก็จะได้เป็น 5 เยอะกำลัง 5 ลบ 3 นะครับ\r\nส่วนตัวนี้เนี่ย ก็คือเอามาบวกกันอยู่แล้ว เพราะว่าเขาคูณกัน\r\nเราจะได้ตัวนี้ออกมานะ เป็น 3 กำลัง 3 ตัวนี้เนี่ย ไม่ต้องไปยุกอะไรกับเขา\r\nเพราะว่าไม่มีตัวไหนที่มีฐานเหมือนกันเลย ส่วนตัวนี้ก็คือ 2 กำลัง 3\r\n3 ตัวนี้นะ แล้วก็บวกกับ 5 คือตัวนี้นะครับ\r\nตัวนี้นะครับ คูณกับ 5 กำลังลบ 3 ใช่ไหม\r\nถ้าเราย้ายขึ้นไปคูณนะ กูขออนุญาตใช้คำนี้ด้วยกัน\r\nเพราะว่าจริง ๆ แล้วใช้คำว่าย้ายขึ้นไปคูณ มันไม่ใช่นะครับ\r\nก็คือมันคุ้นด้วยตัวอินเวิร์ตของเขานั่นเองนะครับ\r\nก็จะได้เป็น\r\n5 เยอะกำลัง 5 รูป 3 นะครับ\r\nสุดท้ายจริง ๆ เราก็จะได้อะไรบ้าง\r\n3 กำลัง 3 คูณ 2 กำลัง 8\r\nคูณ 5 กำลัง 2 นะครับ\r\nตรงตามสิ่งที่โจทย์ต้องการหรือยัง เดี๋ยวเราว่าอะไรบ้าง\r\nให้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกตัวมีเลขชิกกำลังเป็นจำนวนเต็มบวกมีหลายตัวนะ เมื่อกี้เรามี 2 ตัวเดียวใช่ไหม\r\nข้ออธิบาลมาตัวนี้เรามี มีทั้ง 3 มีทั้ง 2 มีทั้ง 5\r\nแล้วเลขชิกกำลังเขาเนี่ย เป็นจำนวนเต็มบวกหรือยัง\r\nหรือยังครับ เป็นเรียบร้อยแล้วนะครับ\r\nเพราะฉะนั้นข้อนี้เนี่ย เราก็\r\nครูbedit ที่ 9 นิดนึงเหล่าความใจ ہوมาว่า นายคงได้จับคำนึงจุดนงค่ะ\r\nเพื่อนลูกคุม beberodenสั่นที่ 5-U\r\n expedit นับประสีทั้งโภกตรด governance\r\nyo doot doot doot\r\ncokor doot\r\nc sixty doot\r\ncokor doot doot\r\ncokor doot doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\nดูนะครับว่ามันจะเป็นอย่างไรบ้าง\r\nสำหรับตัวอย่างนี้ของเรานะครับ\r\nก็จะมีความแตกต่างจากตัวอย่าง\r\n2 ตัวอย่างที่เราทำผ่านมานะครับ\r\nแต่ไอ้ไงก็คือตัวนี้นะครับ\r\nเป็นตัวแปรนะครับ\r\nไม่ใช่ตัวจำนวนเหมือนที่ผ่านมานะครับ\r\nจดข้อนี้บอกว่าอย่างไรบ้าง\r\nให้ x, y และ measure จูดจริงที่ไม่เป็น 0 นะครับ\r\nจงทำให้พ Matth ต่อไปนี้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกจำนวนมีเลขชื่อกำลังเป็นจำนวนเต็มบวก นะครับ\r\nอันนี้คือสิ่งที่โจทย์กำลังถามเรารู้ไหม\r\nอยู่ตรงนี้ครับดังเรียน\r\nx ส่วน y ทั้งหมดกำลัง 3\r\nคูณอยู่กับ y กำลัง 2 x ส่วนด้วย z นะครับ\r\nตัวนี้ไม่มีเลขยกกำลังมาสอนตรงนี้นะ\r\nแต่ตัวนี้มีนะครับ ก็คือยกกำลัง 3 นะครับ\r\nเพราะฉะนั้นวิธีการของเราก็คือเราก็ทำเหมือนกับจำนวนนะครับ\r\nที่เป็นตัวเลขนะ เหมือนปกติเลยก็คือการใจ\r\nเลขชื่อกำลังเข้าไปนะครับ เราก็จะได้ออกมาเป็นดังนี้นะครับ\r\nเป็น x กำลัง 3 ส่วน y กำลัง 3 นะครับ ตามมุมเล็บแรกของเราเลยนะ\r\nส่วนตัวนี้นะครับ เราก็สามารถเอามุมเล็บออกได้นะ\r\nเพราะว่าเป็นเครื่องหมายคูณนะครับ เราไม่ต้องมาใส่เครื่องหมายคูณเข้าไปนะครับ\r\nถ้าเป็นตัวแปลกแบบนี้ก็คือเป็น y กำลัง 2x ส่วนด้วย\r\nz นะตัววงเล็บที่ 2 เรากระจายมาซึ่ง z ก็จะเป็นคูณกับ y กันอัน 3 จากวงเล็บแรกนั่นเองนะครับ\r\nอันดับต่อมานะครับนักเรียนลองคิดตามครูนะว่าสิ่งที่เราต้องการทำนี่เพื่ออะไรบ้าง\r\nยังไม่ไหมที่ครูเคยบอกก็คืออะไร\r\nให้ไปดูว่าฐานของเลขยกกำลังในแต่ละตัวน่ะ มีตัวไหนที่เขาเหมือนกันไหมนะครับ\r\nที่มีค่าเท่ากันไหม นี่ไงครับนักเรียน x\r\nตัวนี้ x กันลัง 3 ตัวนี้ x ยกกำลังอะไร\r\nถ้าเราไม่เขียนก็คือ x ยกกำลัง 1 ครับนักเรียนนะครับ\r\nส่วน y ตัวนี้นะครับ ตัวนี้คือเป็น y กันลัง 2\r\nส่วนด้วย y กำลัง 3 นะครับ\r\nเพราะฉะนั้น 2 ตัวนี้นะครับ เขาคูณกันอยู่\r\nแต่ 2 ตัวนี้นะครับ ตัว y นี้เขาหันกันนะครับ\r\nเพราะฉะนั้นหรือ y กำลัง 2 ส่วนด้วย y กำลัง 3 นั่นเอง\r\nถ้าครูอ่านเฉพาะตัวนี้นะ เพราะฉะนั้นเราก็สามารถกระทำกับ\r\nx กลาง 3 กับ x กลาง 1 ยังไงได้บ้าง\r\nส่วนตัว y เราจะทำยังไงบ้างนะ\r\nนักเรียนลองคิดตามนะว่า คุณครูจะทำยังไงบ้าง\r\nคุณครูทำอย่างนี้ครับ ก็คือ x กำลัง 3 บวก 1\r\nส่วนตัว y นะครับ กำลัง 3 ลบ 2 ตัวนี้คือตัวส่วนนะ\r\nสังเกตเห็นไหมครับ คุณครูจะไม่เอาตัว 3 นะครับ\r\nคูณด้วย y ยกกำลังลบ 3 ตรงนี้นะ\r\nเพราะบางคนก็อาจจะเอาขึ้นไปขึ้นบนตรงนี้นะครับ\r\nเป็นลบ 3 ตรงนี้นะครับ\r\nบางทีพอทำปุ๊บเนี่ย\r\nค่าตรงนี้ไม่ได้ติดลบนะครับ\r\nมันจะกลายเป็น 2 ลบ 3 ก็คือเป็นลบ 1\r\nแต่ว่าข้อนี้เราต้องการเลขชี่กำลังเป็นจำนวนเต็มบวก\r\nดังนั้นเนี่ยคุณครูทำครั้งเดียวไปเลย\r\nก็คือเอา 2 ตรงนี้นะครับ\r\nมาดำเดือนกันก็คือ รบกับ 3 ตรงนี้\r\nเราก็จะได้เป็น y กำลัง 3 รบ 2 นะคะ даже grad\r\nเพราะฉะนั้นนี่ คือนักเรียนต่างคนไม่ถนัด\r\nก็คือถนัดที่จะเอาไปอยู่ข้างบนอย่างเดียวนะ\r\nอย่างนี้ก็ได้นะครับ\r\nไม่ผิดแต่อย่างไร\r\nแต่สุดท้าย อย่าลืมนะ ว่าเลขชีพกำลังของเราทุกตัวนะครับ\r\nจะต้องเป็นเป็นบวกหมดเลย\r\nตรงนี้เราก็จะได้เป็น x กระดัง 4 ส่วนด้วย yz นะครับนักเรียน\r\nเป็นอย่างไรบ้าง เราดูตัวอย่างนะครับ\r\nมาทั้ง 3 มาแล้ว ทั้งตัวอย่างที่เป็นจำนวดที่เป็นตัวเลข\r\nกับตัวอย่างที่เป็นตัวแปรนะครับ เพราะฉะนั้นนี่\r\nนักเรียนไม่ต้องพร้อมคุณอะไรนะครับ\r\nค่อย ๆ ทำไปนะครับ\r\nแล้วก็ค่อย ๆ ดูว่าทฤษฎีอะไรที่เราสามารถนำมาใช้ในแต่ละข้อได้บ้างนะครับ\r\nอ่ะ เรามาดูสิ่งที่เราได้เรียนรู้อะไรบ้างในบทเรียนในวันนี้นะครับ\r\nก็คือ\r\nคุณครูบอกแล้วตอนต้นคลิปนะว่า สิ่งที่เราควรจะรู้มีไหนบ้าง\r\nก็คือวันนี้เราก็จะได้มาทบทวนนะครับ บทนิยามของเขา\r\nซึ่งต้นคลิปคุณครูก็บอกไปแล้ว ก็คือเราก็รู้ว่า\r\nไอ้ตัว a กำลัง n ตรงนี้นะครับ ก็คือเป็นเลขยกกำลังนะ\r\nเรามีความหมายทางนี้ก็คือ ถ้า a กำลัง n ก็คือ a คูณกันไปทั้งหมด n ตัวนะครับ\r\nเราก็จะเรียกว่า a กำลัง n คือเลขยกกำลัง เรียก a ว่าเป็นฐานของเลขยกกำลัง\r\nแล้วก็เรียก n ว่าเป็นเลขชื่อกำลังนะครับ\r\nส่วนนิยามอีก 2 ตัวก็คือ a กำลัง 0 ได้เท่ากับ 1\r\nโดยที่ a ไม่เท่ากับ 0 นะครับ\r\nส่วนอีกอันหนึ่งก็คือ a กำลังลบ n เท่ากับ 1\r\nส่วนด้วย a กำลัง n นะครับ เมื่อ a ไม่เท่ากับ 0 นะครับ\r\nอันนี้คือสิ่งที่เราได้เรียนในวันนี้นะครับ\r\nอีกอันหนึ่งก็คือตัวทฤษฎีบทนะครับ\r\nที่เราได้ทบทวนไปตอนต้นคลิปก็คือ\r\nตัวแรกก็คือตัวนี้นะ\r\nab เป็นยกบันจริงที่ไม่ใช่ 0 แล้วก็ mn เป็นยกบันเต็มนะครับ\r\nเราก็ได้ทั้งหมด 5 ข้อก็คือ a m x a n เท่ากับ a n นะครับ\r\nแล้วก็ข้อ 2 ก็คือ a m ทั้งหมดกำลัง n เราก็จะได้ว่าเท่ากับ na a m n\r\nแล้วก็ข้อ 3 ก็คือ a คูณ b ทั้งหมดยกกำลัง n นะครับ\r\nเราก็จะได้ว่า a กำลัง n คูณกับ b กำลัง n นะครับ\r\nข้อ 4 ก็คือ a ส่วน b ทั้งหมดยกกำลัง n ก็จะเท่ากับ a กำลัง n ส่วนด้วย\r\nมีกำลัง n อันนี้นะครับที่คุณครูได้อธิบายในตรงคลิปไปแล้วแล้วก็ข้อสุดท้ายของเราก็คือ a กำลัง n ส่วนด้วย\r\na กำลัง n จะเท่ากับ a กำลัง m ลบ n นะครับ\r\nอ่า เป็นยังไงบ้างครับนักเรียนคลิปในวันนี้นะครับ\r\nแต่ว่าก่อนที่จะจบคลิปเนี่ยคุณครูอาจจะให้\r\nตัวตัวอย่างและก็แบบฝึกหัดเนี่ยเพื่อให้นักเรียนเนี่ยไปไปฝึกอีกทีนึงนะครับเดี๋ยวเราเจอกันในคลิปหน้านะครับมาดูว่าคุณครูมีอะไรจะมาให้นักเรียนได้ได้เรียนรู้นะครับบ้างนะครับวันนี้ก็ขอจบคลิปไว้เพียงเท่านี้สวัสดีครับ\r\nครับ","time":"2024-09-16T17:14:02+07:00","caller":"/go/src/app/internal/handler/text_improver.go:95"}
{"level":"info","spacing":"สวัสดีครับ คุณครูอยอแมน อิ๋ véritable นะครับ \r\nวันนี้เราจะมาเรียนโบริเศนออนไลน์เรื่องเลขยกกำลังนะครับ \r\nซึ่งเป็นตอนที่ 1 นะครับ \r\nเนื้อหาจะอยู่ในชั้นประเทศอุตสาหร่างปีที่ 5 นะครับ \r\nเรามารู้กันเลยว่า rzecz หามีอะไรบ้าง \r\nแล้วก็เราเรียนแล้วเนี่ย เราจะรู้อะไรได้บ้างนะครับ \r\nไป\r\nไปกันเลย\r\nวัตถุประสงค์ในการเรียนในวันนี้นะครับ \r\nอืม เรามีทั้งหมด 2 ข้อนะ\r\nก็คือทบทวนบริยาม และก็ทบทวนทฤษฎีบทนะครับ \r\nเกี่ยวกับเลขยกกำลังที่มีเลขชื่อกำลังเป็นจำนวนเต็มนะครับ \r\nเพราะฉะนั้น นี่คือวัตถุประสงค์ของการเรียนในคลิปนี้นะครับ \r\nนักเรียนก็ไปดูว่า เนื้อหาที่เราเรียนเนี่ย\r\nจะเป็นอย่างไรบ้างนะครับ \r\nบทนิยามที่ 1 ของเลขยกกำลังนะครับ \r\nให้ a เป็นจำนวนจริง และ n เป็นจำนวนเต็มบวก\r\na ยกกำลัง n หรือ a กำลัง n\r\nคือเราสามารถอ่านได้ทั้ง 2 แบบนะครับ \r\nก็คืออ่านว่า a ยกกำลัง n หรือ\r\na กำลัง n อันทั้ง 2 แบบเลยนะครับ \r\nเขียนแทนด้วย a กำลัง n นะครับ แล้วก็จะมีความหมายอย่างนี้นะ\r\nสำหรับตัวนี้ ก็คือ a กำลัง n ความหมายของเราก็คือ\r\na คูณ a คูณ a คูณไปเรื่อย ๆ นะครับ \r\nคุณไปถึงไหนล่ะ เท่ากับจำนวน n ตัว เท่ากับตัว n ตรงนี้นะครับ \r\nเท่ากับจุดมนต์ตรงนี้นะ เพราะฉะนั้นนะครับ \r\nเราจะเรียก a กับ n นี้นะครับ เรียกทั้งก้อนนี้เลยนะว่าเป็นเลขยกกำลังนะครับ \r\nเราก็จะเรียก a ว่าเป็นฐานของเลขยกกำลัง แล้วก็เราจะเรียก n ว่าเป็นเลขชีกกำลังนะครับ \r\nต่อไปเรียกคูป\r\nคุณครูอาจจะบอกว่าตัว a นี่คือเป็นฐานของเลขยกกำลัง\r\nและก็จะบอกว่า a นี่ก็คือเป็นเลขยกกำลังของเขานะครับ \r\nนี่ยามต่อมามีไหม\r\na กำลัง 0 เท่ากับ 1 นะครับ \r\nแต่ว่ามีเงื่อนไขปุ่มเข้ามาอีกนิดหนึ่งนะครับ \r\nก็คือ a นี่ไม่เท่ากับ 0 นะครับ \r\nบางคนก็จะพูดแบบ\r\nไปเลยว่า a ยกกำลัง 0 เท่ากับ 1\r\na เป็นอะไรก็ได้ จริง ๆ เป็นอะไรก็ได้ ไม่ถูกต้องนะครับ \r\na ของเราจะต้องไม่เท่ากับ 0 ด้วยนะครับ \r\nอันต่อมาก็คือ a\r\nยกกำลังลบ n นะครับ จะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n นะครับ เมื่อ a ไม่เท่ากับ 0 นะครับ นิยามทั้ง 2 ตัวนี้จะมีเงื่อนไขเหมือนกันก็คือ a ไม่เท่ากับ 0 นะครับ นักเรียนต้องระวังด้วยสำหรับข้อนี้นะครับ เรามาดูต่อไปเรามาดูตัว\r\nว่า...\r\nทฤษฎีที่มันเกี่ยนเรื่องกับนิยามบ้างว่าเป็นยังไงบ้างนะครับ \r\nเราไปกันเลย\r\nทฤษฎีบทที่ 1 เลย\r\nเขาว่าให้ a, b เป็นจำนวนจริงที่ไม่เป็น 0\r\nและ m, n เป็นจำนวนเต็ม\r\nเราจะได้ว่านะครับ \r\nข้อ 1 เลย\r\na ยกกำลัง m คูณกับ a\r\nยกกำลัง n เท่ากับ a ยกกำลัง m บวก n นะครับ \r\nสำหรับตัวนี้นะที่สดีบทที่ 1 เนี่ย\r\nข้อที่ 1 นะครับ ของเรา\r\nถ้า a นะครับ ตัวนี้คือเลขชีกกำลังของเขา\r\nและก็ a ตัวนี้เลขยกกำลังเขาคือตัว n นะครับ \r\nถ้า 2 ตัวนี้เราคูณกันนะครับ \r\nเราจะเอาเลขยกกำลังของเขามาบวกกันนะครับ \r\nหรือเรียกง่าย ๆ ก็คือเราเอาทั้ง 2 ตัวนี้มาดำเนินกันโดยการบวกนะครับ \r\nนี่คือข้อแรก\r\nข้อที่ 2 เป็นอย่างไรบ้าง\r\na ยกกำลัง m\r\nทั้งหมดยกกำลัง n จะเท่ากับ a ยกกำลัง m คูณ n นะครับ \r\nซึ่งถ้าเรามีเลขยกกำลังนะครับ ที่มีเลขชิ้นกำลังตรงนี้ซ้อมกันอยู่นะครับ \r\nวิธีการของเราก็คือ\r\nให้เรานำเลขชีกกำลังมาคูณกัน\r\nก็คือเอา m กับ n มาคูณกันและเอกนะครับ \r\nอันนี้คือข้อที่ 2 ส uters ที่สดีบบที่ 1 นะครับ \r\nมาดูข้อที่ 3 กัน\r\nข้อที่ 3a คูณ b ทั้งหมดยกกำลัง n นะครับ \r\nเราจะได้ว่า\r\na ยกกำลัง n คูณกับ b ยกกำลัง n\r\nเราจะสังเกตเห็นว่านะครับ \r\na กับ b ตัวนี้เนี่ย เป็นฐานของเลขยกกำลัง\r\nส่วน n ก็คือจะเป็นเลขชีกกำลังของเขานะครับ \r\nเสร็จแล้ว a กับ b เนี่ย เขาคูณกันอยู่นะครับ \r\nดังนั้นเราจึงกระจายเลขชีกกำลังนะครับ \r\nเข้าไปก็จะได้เป็น a ยกกำลัง n คูณกับ b ยกกำลัง n\r\nแต่มีข้อควรระวังนิดหนึ่งนะ ถ้าตัวนี้เป็นเครื่องหมายบกลบนี่\r\nเราจะไม่กระถับแบบนี้ไปดังขาดนะครับ \r\nเพราะว่าไม่ใช่ทฤษฎีบทที่ 1 ของเลขยกกำลังของเรานะครับ \r\nข้อ 4\r\na ส่วน b ทั้งหมดยกกำลัง n นะครับ \r\nเราจะเห็นว่าเลขชิ้นกำลังของทั้ง a และ b นี่\r\nที่เขาสวดกันอยู่ในคือกำลัง n นะครับ \r\nเราก็สามารถทำได้คล้าย ๆ กับข้อที่ 3 นะครับ \r\nแต่ข้อที่ 3 นี่เขาเป็นเครื่องหมายคูณ\r\nแต่ข้อ 4 นี่เป็นเครื่องหมายหานะครับ \r\nหรือเป็นเสร็จส่วนนั่นเองนะครับ \r\nเราก็จะได้ว่า\r\na ยกกำลัง n หารด้วย b ยกกำลัง n\r\nอันนี้คือ เป็นข้อที่ 4 ของทฤษฎีบทที่ 1 ของเรา\r\nส่วนข้อสุดท้ายคือ ข้อที่ 5 ก็คือ\r\na ยกกำลัง m ส่วนด้วย a ยกกำลัง n\r\nเราก็จะได้ว่า\r\na ยกกำลัง m ลบ n นะครับ \r\nตัวนี้มันเกิดมาจากนิยามของ\r\nนิยามที่ 1 ของเลขยกกำลังด้วยนะครับ \r\nก็คือเขาบอกว่า a ยกกำลังลบ n นะครับ \r\nจะเท่ากับ 1 ส่วนด้วย a ยกกำลัง n\r\nอันนี้เราก็ใช้ตัวบทนิยามเข้ามาช่วยด้วย\r\nเพื่อจะได้ทฤษฎีบทที่ 1 ของข้อ 5 นักเอกนะครับ นักเรียน\r\nทฤษฎีบทที่ 1 ทั้ง 5 ข้อนี้นะครับ \r\nครูจะไม่พิสูจน์ให้นักเรียนได้ดูนะ เพราะว่า\r\nคลิปนี้เป็นคลิปสำหรับการทบทวนนะครับ \r\nเพราะฉะนั้นครูขอไปที่ตัวอย่างเลยแล้วกัน\r\nตัวอย่างแรกของเรามาแล้วนะครับ \r\nโจทย์บอกว่า จงเขียน 8 กำลัง 6 คูณ 4 กำลัง 5\r\nให้อยู่ในรูปอย่างง่ายนะครับ \r\nและเลขยกกำลังทุกจำนวนมีเลขชี้กำลัง\r\nเป็นจำนวนเต็มบวกนะครับ \r\nอันนี้คือสิ่งที่โจทย์กำลังถามออกมาอยู่นะครับ \r\nเพราะฉะนั้นเนี่ย เราก็ต้องมาลองคิดด้วยวิเคราะห์ญิตนิดหนึ่ง denken yet\r\nว่าจากตัวนิยามในพฤษฎีเนี่ย\r\nเราจะสามารถนำอะไรมาใช้ได้บ้างนะครับ \r\nมาดูที่ 8 ก่อนนะครับ \r\n8 เราเรียกว่าฐานเนาะ\r\nส่วน 6 เราเรียกว่าเลขชีกำหลังของเขานะครับ \r\nส่วนนี้ 4 ก็คือเป็นฐาน ส่วน 5 ก็คือเป็นเลขยกกำลังเขานะครับ \r\nสิ่งที่เราจะสามารถนำเลขยกกำลังนี่มาดำเนินการไว้ว่าจะเป็นบวกหรือลบเนี่ย\r\nตัวฐานของเขาต้องเท่ากันก่อนครับ แล้วก็มาลองคิดดูสิครับ ว่า\r\nเอ๊ะ เราจะทำยังไงได้บ้างเนาะ\r\nนักเรียนในหลายคนเนี่ย ถ้านักเรียนคิดว่า\r\nจะลองคิดเองก่อนนะครับ นักเรียนก็ให้หยุดตัวคลิปของคุณครูไว้\r\nแล้วก็ลองทำก่อน แล้วก็ลองมาดูเฉลยของคุณครูด้วย\r\nตามไปด้วยก็ได้นะครับ มันเป็นการฝึกให้นักเรียนได้คิดด้วยนะครับ \r\nเพราะว่าถ้าดูตามคลิปครูไปเรื่อย ๆ บางทีทำให้เราไม่ได้คิดด้วย\r\nอ่ะ มาต่อกันเลยกันเนอะ\r\nในตัว 8 เราลองคิดดูซึ่งครับ ว่า 8 นี่มีอะไรเป็นตัวประกอบเนาะ\r\nมันแยกตัวประกอบได้อย่างไรนะ แล้ว C ล่ะ มีตัวประกอบอะไรบ้าง นะ\r\n8 ก็คืออะไร นะ 2 คูณ 2 คูณ 2\r\nหรือเราเรียกว่าเป็น 2 กำลัง 3 นั่นเอง\r\nส่วนเลข 4 คืออะไร ล่ะ 4 ก็คือ 2 คูณ 2 นะครับ \r\n2 คูณ 2 ได้ 4 ดังนั้นแสดงว่าเราก็สามารถทำเป็นเลขยกกำลังมาได้\r\nแบบนี้นั่นเอง ก็คือ 8 เมื่อกี้ที่คุณครูบอก 2 กำลัง 3 ใช่ไหมครับ \r\nแล้วเราก็มีกำลังสอนก็คือเลขชื่อกำลังตัวนี้ของเราก็คือ 6 นะ\r\n2 ยกกำลัง 3 ตัว 3 ก็คือเป็นเลขชื่อกำลัง 6 ก็เป็นเลขชื่อกำลังนะครับ \r\nส่วนตัวนี้ก็คือ 4 ของเราก็เปลี่ยนมาเป็น 2 ยกกำลัง 2 ทั้งหมดยกกำลัง 5\r\nเราจะสังเกตเห็นว่าทั้ง 2 ตัวนี้นะครับ \r\nมีเลขยกกำลังที่ซ้อนกันอยู่นะครับ \r\nจากทฤษฎีของเราก็จะได้ว่า ให้นำเลขยกกำลังนี้มาคูณกันนะครับ \r\nตัวนี้ก็เอาเลขยกกำลังคูณกันเช่นเดียวกัน\r\nเราจึงได้ตัวนี้ออกมานะครับ \r\nเป็น 2 กำลัง 18 นะครับ ก็คือเกิดมาจาก\r\n3 คูณ 6 นั่นเอง ส่วน 10 ก็คือเกิดมาจาก 2 คูณ 5 นั่นเองนะครับ \r\nหลังจากนั้น เราก็นำมาพิจัยในว่า\r\nทั้ง 2 ตัวนี้ ทั้ง 2 พตนี้ของเรานะครับ \r\nฐานของเขาเหมือนกันไหม ซึ่งก็โชคดีนะ\r\nฐานมันเป็น 2 คนดีนะครับ \r\nพอฐานเป็น 2 แล้วเราก็\r\nเขาบอกว่าอย่างไรนะ ตามทฤษฎีเรา\r\nอืม ให้นำเลขยกกำลังมาบวกกันนั่นเองนะครับ นักเรียน\r\nเพราะฉะนั้นครู ๆ ก็จะได้เป็น 2 ยกกำลัง 18 บวก 10 นะครับ \r\nก็จะได้เป็น 2 ยกกำลัง 28 นะครับ \r\nแต่ยังตอน\r\nโดดบอกอะไรเราบ้าง โดดบอกว่าให้อยู่ในรูปอย่างง่าย\r\nรูปอย่างง่ายได้ยัง ไม่มีอะไรที่จะง่ายกว่านี้แล้วนะครับ \r\nและเลขยกกำลังทุกจำนวน มีเลขยกกำลังเป็นจำนวนเต็มบวก\r\nเออ มีจำนวนเดียวนะครับ \r\nแล้วยกกำลังเป็นจำนวนเต็มบวกไหม 28 เป็นบวกไหมครับ \r\nเป็นจำนวนเต็มบวก\r\nตรงตามที่โจทย์เขาต้องการพอดีนะครับ \r\nเพราะฉะนั้นอันนี้ก็ถือว่าเป็นรูปแบบง่าย ๆ แล้วนะครับ \r\nเดี๋ยวเราลองไปดูตัวอย่างถัดไปดูนะครับ ว่า\r\nจะยากหรือจะง่ายอย่างไรนะครับ \r\nเราก็ให้คิดตามคุณครูไปด้วยนะครับ รังเรียน\r\nตัวอย่างที่ 2 เรามาเรียบร้อยแล้วครับ นักเรียน เป็นอย่างไรบ้าง ตัวอย่างนี้ลองดูซิ โอ้ มีความยากอยู่นิดนึง ไม่เป็นไรครับ นักเรียน ไม่ต้องตกอบตกใจ ไม่ต้องวิตกกังวลอะไรทั้งนั้นครับ เห็นไหมครับ ตัวนี้ โจทย์ว่าอย่างไรบ้าง ลองอ่านโจทย์ต่อนะครับ ช้า ๆ นะครับ \r\nครับ \r\nจงเขียน 6 ส่วน 5 ทั้งหมดกำลัง 3 คูณกับ 10 ตัวลัง 5\r\nให้อยู่ในรูปอย่างง่ายและเลขยกกำลังทุกจำนวน\r\nมีเลขชี้กำลังเป็นจำนวนเป็นบวกนักเรียนลองคิดตามครูไปด้วยนะ\r\nถ้าเกิดว่านักเรียนคนไหนมีกระดาษหรือยังไงก็แล้วแต่นี่\r\nก็ให้หยิบกระดาษขึ้นมาแล้วก็หยุด\r\nคลิปของครูไว้ก็ได้ แล้วก็ลองทำดูก่อนนะครับ ว่ามันเป็นยังไงบ้าง\r\nถ้าใครยังทำไม่ได้ครูจะไกลให้นิดนึงนะ เรามาลองดูครับ \r\n6 นี่คืออะไร ครับ 6 นี่มีอะไรเป็นตัวประกอบบ้าง\r\nก็คือ 3 กับ 2 นี่ 3 คูณ 2 ได้เท่าไรนะ ได้ 6\r\nหรือบางคนว่า คุณครูผมไม่เอา 3 คูณ 2 ได้ไหม เอา 2 คูณ 3\r\nได้ครับ เพราะว่าเรามีอะไรนะ เรามี\r\nสมบัติการสำหรับพี่สำหรับการคูณด้วยนะครับ \r\nเพราะฉะนั้น 6 ของเราจะเอาเป็น 3 พูด 2 หรือ 2 พูด 3\r\nอ่า แล้วแต่นักเรียนเลยครับ ไม่มีปัญหาอะไรอยู่แล้วนะครับ \r\nอ่า สูตรเลข 10 ดูสิครับ ว่าเลข 10 ของเรานี่\r\nถ้าเราจะแยกตัวประกอบนี่ได้อะไรบ้าง \r\nเอ๊ ได้เลยน่ะ อ๋อ\r\nก็คือ 2 × 5 นะครับ \r\nหรือนักเรียนจะบอกว่า 5 × 2 นั่น\r\nโอ้ ตามสบายนะครับ นักเรียน\r\nจะเป็น 5 × 2 3 × 2 × 5 ได้หมดครับ \r\nเพราะเรามีสมบัติของการสำหรับพี่\r\nสำหรับการคลุมนะครับ \r\nเพราะฉะนั้นเนี่ย ครูก็จะ\r\nตาม 2 ตัวนี้ได้ตามอันทันนี้นะครับ \r\n6 ของเราเมื่อกี้ก็คือบอกว่าอะไรนะ 3 คูณ 2 ส่วน 5\r\nทั้งหมดยกกำลัง 3\r\nตัวนี้นะครับ ข้อนี้ดีอย่างหนึ่งคือเราสามารถใช้ทฤษฎีหลายทฤษฎีได้นะครับ \r\nที่ของเราเนี่ย\r\nไม่ว่าจะเป็นทฤษฎีที่คูณกันแล้วสามารถกระจายเลขยกกำลังเข้าไป\r\nแล้วก็ตัวฐานข้างเดียวสามารถกระจายเลขยกกำลัง\r\nเลขชิ้นกำลังของเขาเข้าไปนะ\r\nบางครั้งนี่ครูอาจจะพูดแบบเร็วไปนิดหนึ่งนะ\r\nตัวนี้บอกว่าเป็นเลขยกกำลัง\r\nแต่ความหมายของเลขยกกำลังจริง ๆ แล้วนี่คือมันทั้งก้อนเลยนะครับ \r\nทั้งก้อนนี้เลยนะ\r\nทั้งข้อนนี้เราเรียกว่าเลขยกกำลัง ส่วนตัวนี้เป็นฐานของเขา\r\nส่วนตัวนี้เรียกว่าเลขยกกำลัง บางทีครูก็เผลอนะครับ \r\nมีบ้างเหมือนกัน บอกว่า 3 เป็นเลขยกกำลังอะไรอย่างนี้\r\nจริง ๆ แล้วคำว่าเลขยกกำลังของเรา ถือทั้งข้อนี้นะครับ \r\nตัวนี้เขาเรียกว่าเป็น\r\nเป็นฐาน ส่วน 1 ตัวนี้เรียกว่าเป็นเลขยกกำลัง\r\nถ้าตรงส่วนไหนที่ครู ๆ พูดผิดไปก็ต้องขออภัยนิดนึง\r\nเพราะว่าพูดเร็วมากนะครับ ในส่วนนี้\r\nโอเค เรามาต่อกันเลยแล้วกัน\r\nตัวนี้ของเรานะครับ เราจะสังเกตว่ามันมีหลาย ๆ ตัวนี้ใกล้เคียงกันแล้วนะครับ \r\nเราก็จะได้อะไรนะ\r\nกระจายเลขยกกำลังเข้าไปนะ ตัวนี้ก็กระจายได้นะ\r\nเพราะว่าตัวนี้คือหมายคูณเหมือนกัน เราจะได้ตัวนี้ออกมา\r\n3 ยกกำลัง 3 คูณ 2 กำลัง 3 หารด้วย 5 กำลัง 3\r\nตามมุมเล็บนี้เลยนะครับ ส่วนตัวนี้นะครับ \r\nคูณกับ 2 กำลัง 5 คูณกับ\r\n5 กำลัง 5 นะครับ จากวงลิฟต์นี้ด้วย\r\nสิ่งที่ตามมาเรามาดูก่อนว่า ตัวไหนที่มีฐานเหมือนกันบ้าง\r\nนี่ไงครับ 2 กำลัง 3 กับ 2 กำลัง 5\r\nมีฐานเหมือนกัน แล้วยังไงต่อครับ \r\nเขาคูณกันครับ \r\nเขาคูณกัน เขาไม่ได้หารกัน\r\nแล้วมีอีกไหม มีอีกไหม\r\nมีครับ มีอย่างไรครับ มี 5 นี่ไง มีอีก\r\nเพราะฉะนั้นตัวนี้เป็นอย่างไรบ้างครับ \r\nตัวนี้\r\nเขาหารกันครับ เขาหาร เขาไม่ได้คูณ\r\nเพราะฉะนั้นถ้าหารกันทำอย่างไรนะ\r\nให้เราดำเนินการโดยนำเลขชิ้นกำลังมามาลบกันใช่ไหมครับ \r\nถ้าเราเอา 5 กำลัง 3 นี่ ขึ้นไปคูณกับตัวนี้นะครับ \r\nมันก็จะได้เป็น 5 เยอะกำลัง 5 ลบ 3 นะครับ \r\nส่วนตัวนี้เนี่ย ก็คือเอามาบวกกันอยู่แล้ว เพราะว่าเขาคูณกัน\r\nเราจะได้ตัวนี้ออกมานะ เป็น 3 กำลัง 3 ตัวนี้เนี่ย ไม่ต้องไปยุกอะไรกับเขา\r\nเพราะว่าไม่มีตัวไหนที่มีฐานเหมือนกันเลย ส่วนตัวนี้ก็คือ 2 กำลัง 3\r\n3 ตัวนี้นะ แล้วก็บวกกับ 5 คือตัวนี้นะครับ \r\nตัวนี้นะครับ คูณกับ 5 กำลังลบ 3 ใช่ไหม\r\nถ้าเราย้ายขึ้นไปคูณนะ กูขออนุญาตใช้คำนี้ด้วยกัน\r\nเพราะว่าจริง ๆ แล้วใช้คำว่าย้ายขึ้นไปคูณ มันไม่ใช่นะครับ \r\nก็คือมันคุ้นด้วยตัวอินเวิร์ตของเขานั่นเองนะครับ \r\nก็จะได้เป็น\r\n5 เยอะกำลัง 5 รูป 3 นะครับ \r\nสุดท้ายจริง ๆ เราก็จะได้อะไรบ้าง \r\n3 กำลัง 3 คูณ 2 กำลัง 8\r\nคูณ 5 กำลัง 2 นะครับ \r\nตรงตามสิ่งที่โจทย์ต้องการหรือยัง เดี๋ยวเราว่าอะไรบ้าง \r\nให้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกตัวมีเลขชิกกำลังเป็นจำนวนเต็มบวกมีหลายตัวนะ เมื่อกี้เรามี 2 ตัวเดียวใช่ไหม\r\nข้ออธิบาลมาตัวนี้เรามี มีทั้ง 3 มีทั้ง 2 มีทั้ง 5\r\nแล้วเลขชิกกำลังเขาเนี่ย เป็นจำนวนเต็มบวกหรือยัง\r\nหรือยังครับ เป็นเรียบร้อยแล้วนะครับ \r\nเพราะฉะนั้นข้อนี้เนี่ย เราก็\r\nครู bedit ที่ 9 นิดนึงเหล่าความใจ ہوมาว่า นายคงได้จับคำนึงจุดนงค่ะ \r\nเพื่อนลูกคุม beberoden สั่นที่ 5-U\r\n expedit นับประสีทั้งโภกตรด governance\r\nyo doot doot doot\r\ncokor doot\r\nc sixty doot\r\ncokor doot doot\r\ncokor doot doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\ncokor doot\r\nดูนะครับ ว่ามันจะเป็นอย่างไรบ้าง\r\nสำหรับตัวอย่างนี้ของเรานะครับ \r\nก็จะมีความแตกต่างจากตัวอย่าง\r\n2 ตัวอย่างที่เราทำผ่านมานะครับ \r\nแต่ไอ้ไงก็คือตัวนี้นะครับ \r\nเป็นตัวแปรนะครับ \r\nไม่ใช่ตัวจำนวนเหมือนที่ผ่านมานะครับ \r\nจดข้อนี้บอกว่าอย่างไรบ้าง\r\nให้ x, y และ measure จูดจริงที่ไม่เป็น 0 นะครับ \r\nจงทำให้พ Matth ต่อไปนี้อยู่ในรูปอย่างง่าย\r\nและเลขยกกำลังทุกจำนวนมีเลขชื่อกำลังเป็นจำนวนเต็มบวก นะครับ \r\nอันนี้คือสิ่งที่โจทย์กำลังถามเรารู้ไหม\r\nอยู่ตรงนี้ครับ ดังเรียน\r\nx ส่วน y ทั้งหมดกำลัง 3\r\nคูณอยู่กับ y กำลัง 2 x ส่วนด้วย z นะครับ \r\nตัวนี้ไม่มีเลขยกกำลังมาสอนตรงนี้นะ\r\nแต่ตัวนี้มีนะครับ ก็คือยกกำลัง 3 นะครับ \r\nเพราะฉะนั้นวิธีการของเราก็คือเราก็ทำเหมือนกับจำนวนนะครับ \r\nที่เป็นตัวเลขนะ เหมือนปกติเลยก็คือการใจ\r\nเลขชื่อกำลังเข้าไปนะครับ เราก็จะได้ออกมาเป็นดังนี้นะครับ \r\nเป็น x กำลัง 3 ส่วน y กำลัง 3 นะครับ ตามมุมเล็บแรกของเราเลยนะ\r\nส่วนตัวนี้นะครับ เราก็สามารถเอามุมเล็บออกได้นะ\r\nเพราะว่าเป็นเครื่องหมายคูณนะครับ เราไม่ต้องมาใส่เครื่องหมายคูณเข้าไปนะครับ \r\nถ้าเป็นตัวแปลกแบบนี้ก็คือเป็น y กำลัง 2x ส่วนด้วย\r\nz นะตัววงเล็บที่ 2 เรากระจายมาซึ่ง z ก็จะเป็นคูณกับ y กันอัน 3 จากวงเล็บแรกนั่นเองนะครับ \r\nอันดับต่อมานะครับ นักเรียนลองคิดตามครูนะว่าสิ่งที่เราต้องการทำนี่เพื่ออะไรบ้าง \r\nยังไม่ไหมที่ครูเคยบอกก็คืออะไร \r\nให้ไปดูว่าฐานของเลขยกกำลังในแต่ละตัวน่ะ มีตัวไหนที่เขาเหมือนกันไหมนะครับ \r\nที่มีค่าเท่ากันไหม นี่ไงครับ นักเรียน x\r\nตัวนี้ x กันลัง 3 ตัวนี้ x ยกกำลังอะไร\r\nถ้าเราไม่เขียนก็คือ x ยกกำลัง 1 ครับ นักเรียนนะครับ \r\nส่วน y ตัวนี้นะครับ ตัวนี้คือเป็น y กันลัง 2\r\nส่วนด้วย y กำลัง 3 นะครับ \r\nเพราะฉะนั้น 2 ตัวนี้นะครับ เขาคูณกันอยู่\r\nแต่ 2 ตัวนี้นะครับ ตัว y นี้เขาหันกันนะครับ \r\nเพราะฉะนั้นหรือ y กำลัง 2 ส่วนด้วย y กำลัง 3 นั่นเอง\r\nถ้าครูอ่านเฉพาะตัวนี้นะ เพราะฉะนั้นเราก็สามารถกระทำกับ\r\nx กลาง 3 กับ x กลาง 1 ยังไงได้บ้าง\r\nส่วนตัว y เราจะทำยังไงบ้างนะ\r\nนักเรียนลองคิดตามนะว่า คุณครูจะทำยังไงบ้าง\r\nคุณครูทำอย่างนี้ครับ ก็คือ x กำลัง 3 บวก 1\r\nส่วนตัว y นะครับ กำลัง 3 ลบ 2 ตัวนี้คือตัวส่วนนะ\r\nสังเกตเห็นไหมครับ คุณครูจะไม่เอาตัว 3 นะครับ \r\nคูณด้วย y ยกกำลังลบ 3 ตรงนี้นะ\r\nเพราะบางคนก็อาจจะเอาขึ้นไปขึ้นบนตรงนี้นะครับ \r\nเป็นลบ 3 ตรงนี้นะครับ \r\nบางทีพอทำปุ๊บเนี่ย\r\nค่าตรงนี้ไม่ได้ติดลบนะครับ \r\nมันจะกลายเป็น 2 ลบ 3 ก็คือเป็นลบ 1\r\nแต่ว่าข้อนี้เราต้องการเลขชี่กำลังเป็นจำนวนเต็มบวก\r\nดังนั้นเนี่ยคุณครูทำครั้งเดียวไปเลย\r\nก็คือเอา 2 ตรงนี้นะครับ \r\nมาดำเดือนกันก็คือ รบกับ 3 ตรงนี้\r\nเราก็จะได้เป็น y กำลัง 3 รบ 2 นะคะ даже grad\r\nเพราะฉะนั้นนี่ คือนักเรียนต่างคนไม่ถนัด\r\nก็คือถนัดที่จะเอาไปอยู่ข้างบนอย่างเดียวนะ\r\nอย่างนี้ก็ได้นะครับ \r\nไม่ผิดแต่อย่างไร\r\nแต่สุดท้าย อย่าลืมนะ ว่าเลขชีพกำลังของเราทุกตัวนะครับ \r\nจะต้องเป็นเป็นบวกหมดเลย\r\nตรงนี้เราก็จะได้เป็น x กระดัง 4 ส่วนด้วย yz นะครับ นักเรียน\r\nเป็นอย่างไรบ้าง เราดูตัวอย่างนะครับ \r\nมาทั้ง 3 มาแล้ว ทั้งตัวอย่างที่เป็นจำนวดที่เป็นตัวเลข\r\nกับตัวอย่างที่เป็นตัวแปรนะครับ เพราะฉะนั้นนี่\r\nนักเรียนไม่ต้องพร้อมคุณอะไรนะครับ \r\nค่อย ๆ ทำไปนะครับ \r\nแล้วก็ค่อย ๆ ดูว่าทฤษฎีอะไรที่เราสามารถนำมาใช้ในแต่ละข้อได้บ้างนะครับ \r\nอ่ะ เรามาดูสิ่งที่เราได้เรียนรู้อะไรบ้าง 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ทั้งหมดยกกำลัง n นะครับ \r\nเราก็จะได้ว่า a กำลัง n คูณกับ b กำลัง n นะครับ \r\nข้อ 4 ก็คือ a ส่วน b ทั้งหมดยกกำลัง n ก็จะเท่ากับ a กำลัง n ส่วนด้วย\r\nมีกำลัง n อันนี้นะครับ ที่คุณครูได้อธิบายในตรงคลิปไปแล้วแล้วก็ข้อสุดท้ายของเราก็คือ a กำลัง n ส่วนด้วย\r\na กำลัง n จะเท่ากับ a กำลัง m ลบ n นะครับ \r\nอ่า เป็นยังไงบ้างครับ นักเรียนคลิปในวันนี้นะครับ \r\nแต่ว่าก่อนที่จะจบคลิปเนี่ยคุณครูอาจจะให้\r\nตัวตัวอย่างและก็แบบฝึกหัดเนี่ยเพื่อให้นักเรียนเนี่ยไปไปฝึกอีกทีนึงนะครับ เดี๋ยวเราเจอกันในคลิปหน้านะครับ มาดูว่าคุณครูมีอะไรจะมาให้นักเรียนได้ได้เรียนรู้นะครับ บ้างนะครับ วันนี้ก็ขอจบคลิปไว้เพียงเท่านี้สวัสดีครับ \r\nครับ ","time":"2024-09-16T17:14:02+07:00","caller":"/go/src/app/internal/handler/text_improver.go:95"}
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