Simplify the Radical Expression (8^(2/3))^4

${(8^{\frac{2}{3}})}^{4}$

Multiply the exponents in ${(8^{\frac{2}{3}})}^{4}$ .

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

$8^{\frac{2}{3} \cdot 4}$

Multiply $\frac{2}{3} \cdot 4$ .

Combine $\frac{2}{3}$ and $4$ .

$8^{\frac{2 \cdot 4}{3}}$

Multiply $2$ by $4$ .

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{8}$

Raise $2$ to the power of $8$ .

$256$