Simplify cube root of 128x^5

$\sqrt[3]{128 x^{5}}$

Step 1

Rewrite $128 x^{5}$ as ${(4 x)}^{3} \cdot (2 x^{2})$ .

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x^{5}}$

Rewrite $64$ as $4^{3}$ .

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

Factor out $x^{3}$ .

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

Move $2$ .

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

Rewrite $4^{3} x^{3}$ as ${(4 x)}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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