Simplify cube root of 54x^4

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Algebra

$\sqrt[3]{54 x^{4}}$

Rewrite $54 x^{4}$ as ${(3 x)}^{3} \cdot (2 x)$ .

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Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{4}}$

Rewrite $27$ as $3^{3}$ .

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

Factor out $x^{3}$ .

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

Move $2$ .

$\sqrt[3]{3^{3} x^{3} \cdot 2 x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

$3 x \sqrt[3]{2 x}$

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