Evaluate (-125)^(-2/3)

${(- 125)}^{- \frac{2}{3}}$

Step 1

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

$\frac{1}{{(- 125)}^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

Rewrite $- 125$ as ${(- 5)}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $- 5$ to the power of $2$ .

$\frac{1}{25}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$