Simplify cube root of -27x^4

$\sqrt[3]{- 27 x^{4}}$

Step 1

Rewrite $- 27 x^{4}$ as ${(- 3 x)}^{3} x$ .

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

Factor out $x^{3}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

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