Simplify cube root of 16x^9

$\sqrt[3]{16 x^{9}}$

Step 1

Rewrite $16 x^{9}$ as ${(2 x^{3})}^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) x^{9}}$

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

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

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

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

Move $2$ .

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

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

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

Step 2

Pull terms out from under the radical.

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