Simplify (-243)^(-1/5)

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

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

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

Simplify the denominator.

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

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{- 3}$

Move the negative in front of the fraction.

$- \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$