Evaluate (-243)^(-2/5)

${(- 243)}^{- \frac{2}{5}}$

Step 1

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

$\frac{1}{{(- 243)}^{\frac{2}{5}}}$

Step 2

Simplify the denominator.

Rewrite $- 243$ as ${(- 3)}^{5}$ .

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$\frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$