Simplify cube root of (-2a)^4

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

Apply the product rule to $- 2 a$ .

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

Raise $- 2$ to the power of $4$ .

$\sqrt[3]{16 a^{4}}$

Rewrite $16 a^{4}$ as ${(2 a)}^{3} \cdot (2 a)$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) a^{4}}$

Rewrite $8$ as $2^{3}$ .

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

Factor out $a^{3}$ .

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

Move $2$ .

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

Rewrite $2^{3} a^{3}$ as ${(2 a)}^{3}$ .

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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