Simplify cube root of -216x^4

$\sqrt[3]{- 216 x^{4}}$

Rewrite $- 216 x^{4}$ as ${(- 6 x)}^{3} x$ .

Rewrite $- 216$ as ${(- 6)}^{3}$ .

$\sqrt[3]{{(- 6)}^{3} x^{4}}$

Factor out $x^{3}$ .

$\sqrt[3]{{(- 6)}^{3} (x^{3} x)}$

Rewrite ${(- 6)}^{3} x^{3}$ as ${(- 6 x)}^{3}$ .

$\sqrt[3]{{(- 6 x)}^{3} x}$

$\sqrt[3]{{(- 6 x)}^{3} x}$

Pull terms out from under the radical.

$- 6 x \sqrt[3]{x}$

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