Simplify (27^(-1/3))^2

${(27^{- \frac{1}{3}})}^{2}$

Multiply the exponents in ${(27^{- \frac{1}{3}})}^{2}$ .

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

$27^{- \frac{1}{3} \cdot 2}$

Multiply $- \frac{1}{3} \cdot 2$ .

Multiply $2$ by $- 1$ .

$27^{- 2 (\frac{1}{3})}$

Combine $- 2$ and $\frac{1}{3}$ .

$27^{\frac{- 2}{3}}$

Move the negative in front of the fraction.

$27^{- \frac{2}{3}}$

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

$\frac{1}{27^{\frac{2}{3}}}$

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3^{2}}$

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

$\frac{1}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$