### Home > PC3 > Chapter 3 > Lesson 3.1.3 > Problem3-43

3-43.

Rewrite each expression below with the smallest possible integer base.
Example: $\frac{1}{9^4}=\frac{1}{(3^2)^4}=\frac{1}{3^8}=3^{-​8}$

1. $\frac { 1 } { 27 ^ { 5 } }$

$\frac{1}{(3^3)^5}$

1. $\left(\frac{1}{8}\right)^x$

$8^{-x}$

1. $16^x\left(\frac{1}{32}\right)^{(2-​x)}$

Rewrite $16$ and $32$ each as a power of $2$.

$(2^4)^x\left(\frac{1}{2^5}\right)^{(2-x)}$

$2^{4x}\left(2^{-5}\right)^{(2-x)}$

$2^{4x}\cdot 2^{-10+5x}$