Simplify cube root of 128x^7

$\sqrt[3]{128 x^{7}}$

Step 1

Rewrite $128 x^{7}$ as ${(4 x^{2})}^{3} \cdot (2 x)$ .

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x^{7}}$

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

$\sqrt[3]{4^{3} \cdot 2 x^{7}}$

Factor out $x^{6}$ .

$\sqrt[3]{4^{3} \cdot 2 (x^{6} x)}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

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

Move $2$ .

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

Rewrite $4^{3} {(x^{2})}^{3}$ as ${(4 x^{2})}^{3}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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