Simplify the Radical Expression (32^3)^(1/5)

${(32^{3})}^{\frac{1}{5}}$

Multiply the exponents in ${(32^{3})}^{\frac{1}{5}}$ .

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

$32^{3 (\frac{1}{5})}$

Combine $3$ and $\frac{1}{5}$ .

$32^{\frac{3}{5}}$

Rewrite $32$ as $2^{5}$ .

${(2^{5})}^{\frac{3}{5}}$

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

$2^{5 (\frac{3}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$2^{5 (\frac{3}{5})}$

Rewrite the expression.

$2^{3}$

Raise $2$ to the power of $3$ .

$8$