# How do you simplify (-32)^(-3/5)?

Oct 13, 2016

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

#### Explanation:

There are two laws of indices in place here.

${x}^{-} m = \frac{1}{x} ^ m \text{ and } {x}^{\frac{p}{q}} = {\left(\sqrt[q]{x}\right)}^{p}$

Use the sign law first to make the index positive.

1/((-32)^(3/5)

Change the index to a root and a power:

$= \frac{1}{\textcolor{red}{\sqrt[5]{\left(- 32\right)}}} ^ \left(3\right) \text{ } \leftarrow$ find 5th root of -32

$= \frac{1}{{\left(- 2\right)}^{3}} \text{ } \leftarrow$ find the cube of -2

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