6:=(3/2)*(3/2)^2*(3/2)^4=(3/2)^7

7: =(1/2)^7*2^3*2^5*2^8=2^9

8: =(-1/7)^4*5^4=(-5/7)^4

9: =2^2*2^5:(2^3/2^4)

=2^7/2=2^6

10: =(1/7)^3*7^2=1/7

a: \(A=8^2\cdot32^4=2^6\cdot2^{20}=2^{26}\)

b: \(B=27^3\cdot9^4\cdot243=3^9\cdot3^8\cdot3^5=3^{22}\)

\(8^4.16^5.32=2^{3.4}.2^{4.5}.2^5=2^{12}.2^{20}.2^5=2^{12+20+5}=2^{37}\)

8⁴.16⁵.32=2^4.3.2^4.5.2⁵= 2^12+20+5=2²⁷

^{( nhớ tick đúng cho mình nha)}

8^4 . 16^5 . 32 = 2^3.4 . 2^4.5 . 2^5 = 2^12 . 2^20 . 2^5 = 2^37

\(\dfrac{1}{32}\) = 2^-5

\(\dfrac{1}{32}\) = 2^-5

\(\dfrac{1}{8}\) = 2^-3

0,5 = \(\dfrac{1}{2}\) = 2^-1

0,25 = \(\dfrac{1}{4}\) = 2^-2

`@` `\text {Ans}`

`\downarrow`

`-1/27 = ( (-1)^3/(-3)^3) =(-1/3)^3`

`8/729 = ( (2^3)/(9^3) ) = (2/9)^3`

`16/685 = ( (4^2)/( \sqrt {685}) ) = (4/(\sqrt {685}) )^2`

\(\frac{-1}{8}=\frac{-1}{2}\cdot\frac{-1}{2}\cdot\frac{-1}{2}=\left[\frac{-1}{2}\right]^3\)

\(\frac{1}{16}=\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\left[\frac{1}{2}\right]^4\)

Dương bạn nên sửa -1/16 thành 1/16 nhé

Vì -1/16 không phải là một số viết dưới dạng lũy thừa nhé

Bài làm

\(\left(-\frac{1}{8}\right)=\left(-\frac{1}{2}\right)^3\)

\(\left(\frac{1}{16}\right)=\left(\frac{1}{2}\right)^4\)

# Chúc bạn học tốt #

\(\frac{-1}{8}=\left(\frac{-1}{2}\right)^3\)

\(A=8^4.16^5.32=\left(2^3\right)^4.\left(2^4\right)^5.2^5\)\(=2^{12}.2^{20}.2^5=2^{12+20+5}=2^{37}\)

Vậy \(A=2^{37}\)

\(B=27^4.81^{10}=\left(3^3\right)^4.\left(3^4\right)^{10}=3^{12}.3^{40}=3^{12+40}=3^{52}\)

Vậy \(B=3^{52}\)

a)\(4^3.2^4\div\left(4^2.\frac{1}{32}\right)\)

\(=\left(2^2\right)^3.2^4\div\left(2^2\right)^2\div32\).

\(=2^{\left(2.3\right)}.2^4\div2^{\left(2.2\right)}\div2^5\)

\(=2^6.2^4\div2^4\div2^5\)

\(=2^{6+4-4-5}=2^1\)

b)\(\left(\frac{1}{5}\right)^5=\frac{1}{5^5}=\left|5^5\right|=5^{-5}\)

\(\frac{1}{125}=\frac{1}{5^3}=\left|5^3\right|=5^{-3}\)

c)\(\frac{4}{25}=\frac{2^2}{5^2}=\left(\frac{2}{5}\right)^2=0,4^2\)

\(\frac{-8}{125}=\frac{-2^3}{5^3}=\left(\frac{-2}{5}\right)^2=-0,4^3=0,4^{-3}\)

\(\frac{16}{625}=\frac{2^4}{5^4}=\left(\frac{2}{5}\right)^4=0,4^4\)