Simplify cube root of 64x^4

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

Step 1

Rewrite $64 x^{4}$ as ${(4 x)}^{3} x$ .

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

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

Factor out $x^{3}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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