Evaluate (8^2)^(1/3)

${(8^{2})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(8^{2})}^{\frac{1}{3}}$ .

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

$8^{2 (\frac{1}{3})}$

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

$8^{\frac{2}{3}}$

Rewrite $8$ as $2^{3}$ .

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

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

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

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{2}$

Step 3

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

$4$