Simplify cube root of 16x^4

$\sqrt[3]{16 x^{4}}$

Step 1

Rewrite $16 x^{4}$ as ${(2 x)}^{3} \cdot (2 x)$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) x^{4}}$

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

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

Factor out $x^{3}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

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