Simplify cube root of 54a^4

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

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

Factor $27$ out of $54$ .

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

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

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

Factor out $a^{3}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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