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

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$