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

${(- 32)}^{- \frac{3}{5}}$

Step 1

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

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

Step 2

Simplify the denominator.

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

$\frac{1}{{({(- 2)}^{5})}^{\frac{3}{5}}}$

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

$\frac{1}{{(- 2)}^{5 (\frac{3}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{{(- 2)}^{5 (\frac{3}{5})}}$

Rewrite the expression.

$\frac{1}{{(- 2)}^{3}}$

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

$\frac{1}{- 8}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{8}$

Decimal Form:

$- 0.125$