Question

Simplify:

${\displaystyle \sqrt[5]{{\left(32\right)}^{-3}}}$

Answer 1

Given ${\displaystyle \sqrt[5]{{\left(32\right)}^{-3}}}$

${\displaystyle =\sqrt[5]{{\left(\frac{1}{32}\right)}^3}}$

${\displaystyle ={\left(\frac{1}{32}\right)}^{\frac{3}{5}}}$

${\displaystyle ={\left(\frac{1}{{\left(2\right)}^5}\right)}^{\frac{3}{5}}}$

${\displaystyle ={\left(\frac{1}{2}\right)}^{5\times \frac{3}{5}}}$

${\displaystyle ={\left(\frac{1}{2}\right)}^3}$

${\displaystyle =\frac{1}{8}}$