Evaluate (1/(512^(-1/3)))

$(\frac{1}{512^{- \frac{1}{3}}})$

Step 1

Simplify the expression.

Move $512^{- \frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$512^{\frac{1}{3}}$

Rewrite $512$ as $8^{3}$ .

${(8^{3})}^{\frac{1}{3}}$

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

$8^{3 (\frac{1}{3})}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$8^{3 (\frac{1}{3})}$

Rewrite the expression.

$8^{1}$

Step 3

Evaluate the exponent.

$8$