Simplify cube root of 32x^9

$\sqrt[3]{32 x^{9}}$

Step 1

Rewrite $32 x^{9}$ as ${(2 x^{3})}^{3} \cdot 4$ .

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4) x^{9}}$

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

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

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

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

Move $4$ .

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

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

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

Step 2

Pull terms out from under the radical.

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