Evaluate 1/(( fifth root of -32)^-3)

$\frac{1}{{(\sqrt[5]{- 32})}^{- 3}}$

Step 1

Move ${(\sqrt[5]{- 32})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${\sqrt[5]{- 32}}^{3}$

Step 2

Rewrite $- 32$ as ${(- 2)}^{5}$ .

${\sqrt[5]{{(- 2)}^{5}}}^{3}$

Step 3

Pull terms out from under the radical, assuming real numbers.

${(- 2)}^{3}$

Step 4

Raise $- 2$ to the power of $3$ .

$- 8$