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Các dạng bài tập về lũy thừa với số mũ tự nhiên

Các dạng bài tập về lũy thừa với số mũ tự nhiên

ꦐTổng hợp đề thi học kì 2 lớp 6 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên...
Quảng cáo

I. Viết gọn một tích, một phép tính dưới dạng một lũy thừa

Phương pháp giải

 Áp dụng công thức:  $\underbrace {a.a.a.....a}_{n\,{\rm{thua}}\,{\rm{so}}}$$ = {a^n};$${a^m}.{a^n} = {a^{m + n}};{a^m}:{a^n} = {a^{m - n}}\left( {a \ne 0,m \ge n} \right)$

II. Nhân và chia hai lũy thừa cùng cơ số

Phương pháp giải

Bước 1: Xác định cơ số và số mũ.

Bước 2:ไ Áp dụng công thức:${a^m}.{a^n} = {a^{m + n}};{a^m}:{a^n} = {a^{m - n}}\left( {a \ne 0,m \ge n} \right)$

III. So sánh các số viết dưới dạng lũy thừa

Phương pháp giải

Để so sánh các số viết dưới dạng lũy thừa, ta có thể làm theo:

Cách 1:ꩲ Đưa về cùng cơ số là số tự nhiên, rồi so sánh hai số mũ

Nếu \(m > n\) thì \({a^m} > {a^n}\)

Cách 2: Đưa về cùng số mũ rồi so sánh hai cơ số

Nếu \(a > b\) thì \({a^m} > {b^m}\)

Cách 3: Tính cụ thể rồi so sánh

Ngoài ra ta còn sử dụng tính chất bắc cầu: Nếu \(a < b;b < c\) thì \(a < c.\)  

IV. Tìm số mũ của một lũy thừa trong một đẳng thức

Phương pháp giải

Bước 1: Đưa về hai luỹ thừa của cùng một cơ số.

Bước 2: Sử dụng tính chất 

Với \(a \ne 0;a \ne 1\), nếu ${a^m} = {a^n}$ thì $m = n\,\,(a,m,n \in N)$

V. Tìm cơ số của lũy thừa

Phương pháp giải

Cách 1: Dùng định nghĩa lũy thừa

$\underbrace {a.a.....a}_{n\,{\rm{thừa}}\,{\rm{số}}\,a}$ $ = {a^n}$
Cách 2: Sử dụng tính chất

Với \(a;b \ne 0;a;b \ne 1\), nếu ${a^m} = {b^m}$ thì $a = n\,\,(a,b,m,n \in N)$.

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