# How do you simplify 32^(-2/5)?

Jan 26, 2017

$\frac{1}{4}$

#### Explanation:

Recall that:

${a}^{-} b = \frac{1}{a} ^ b$

and

${a}^{\frac{b}{c}} = \sqrt[c]{{a}^{b}}$

combined, it is ${a}^{- \frac{b}{c}} = \frac{1}{\sqrt[c]{{a}^{b}}}$

The above apply where defined.

Therefore, 32^(-2/5) = 1/(root(5)(32^2)

=1/((root(5)(32))^2 $= \frac{1}{2} ^ 2 = \frac{1}{4}$, because ${\textcolor{red}{2}}^{5} = 32$.