Simplify cube root of 32x^5

$\sqrt[3]{32 x^{5}}$

Rewrite $32 x^{5}$ as ${(2 x)}^{3} \cdot (4 x^{2})$ .

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4) x^{5}}$

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

$\sqrt[3]{2^{3} \cdot 4 x^{5}}$

Factor out $x^{3}$ .

$\sqrt[3]{2^{3} \cdot 4 (x^{3} x^{2})}$

Move $4$ .

$\sqrt[3]{2^{3} x^{3} \cdot 4 x^{2}}$

Rewrite $2^{3} x^{3}$ as ${(2 x)}^{3}$ .

$\sqrt[3]{{(2 x)}^{3} \cdot 4 x^{2}}$

Add parentheses.

$\sqrt[3]{{(2 x)}^{3} \cdot (4 x^{2})}$

Pull terms out from under the radical.

$2 x \sqrt[3]{4 x^{2}}$