Evaluate (1/(216^(-2/3)))

$(\frac{1}{216^{- \frac{2}{3}}})$

Simplify the expression.

Move $216^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$216^{\frac{2}{3}}$

Rewrite $216$ as $6^{3}$ .

${(6^{3})}^{\frac{2}{3}}$

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

$6^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$6^{3 (\frac{2}{3})}$

Rewrite the expression.

$6^{2}$

Raise $6$ to the power of $2$ .

$36$