Simplify cube root of 16x^3

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

Step 1

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

Factor $8$ out of $16$ .

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

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

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

Move $2$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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