Simplify cube root of 64a^16

$\sqrt[3]{64 a^{16}}$

Step 1

Rewrite $64 a^{16}$ as ${(4 a^{5})}^{3} a$ .

Rewrite $64$ as $4^{3}$ .

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

Factor out $a^{15}$ .

$\sqrt[3]{4^{3} (a^{15} a)}$

Rewrite $a^{15}$ as ${(a^{5})}^{3}$ .

$\sqrt[3]{4^{3} ({(a^{5})}^{3} a)}$

Rewrite $4^{3} {(a^{5})}^{3}$ as ${(4 a^{5})}^{3}$ .

$\sqrt[3]{{(4 a^{5})}^{3} a}$

Step 2

Pull terms out from under the radical.

$4 a^{5} \sqrt[3]{a}$