Simplify cube root of 128x^9

$\sqrt[3]{128 x^{9}}$

Step 1

Rewrite $128 x^{9}$ as ${(4 x^{3})}^{3} \cdot 2$ .

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x^{9}}$

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

$\sqrt[3]{4^{3} \cdot 2 x^{9}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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