Simplify cube root of 256x^3

$\sqrt[3]{256 x^{3}}$

Step 1

Rewrite $256 x^{3}$ as ${(4 x)}^{3} \cdot 4$ .

Factor $64$ out of $256$ .

$\sqrt[3]{64 (4) x^{3}}$

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

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

Move $4$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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