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

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

Simplify the expression.

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

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

$8^{\frac{1}{3} \cdot 2}$

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

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{2}$

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

$4$