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

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

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

Simplify the expression.

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

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

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

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{1}$

Step 4

Evaluate the exponent.

$3$