Simplify cube root of -64x^5

$\sqrt[3]{- 64 x^{5}}$

Step 1

Rewrite $- 64 x^{5}$ as ${(- 4 x)}^{3} x^{2}$ .

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

$\sqrt[3]{{(- 4)}^{3} x^{5}}$

Factor out $x^{3}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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