Evaluate 32^(-2/5)

$32^{- \frac{2}{5}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{32^{\frac{2}{5}}}$

Step 2

Simplify the denominator.

Rewrite $32$ as $2^{5}$ .

$\frac{1}{{(2^{5})}^{\frac{2}{5}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{2^{5 (\frac{2}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{2^{5 (\frac{2}{5})}}$

Rewrite the expression.

$\frac{1}{2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$