Evaluate (-27)^(-1/3)

${(- 27)}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(- 27)}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{- 3}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$