Simplify cube root of 64a^6b^7c^9

$\sqrt[3]{64 a^{6} b^{7} c^{9}}$

Step 1

Rewrite $64 a^{6} b^{7} c^{9}$ as ${(4 a^{2} b^{2} c^{3})}^{3} b$ .

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

$\sqrt[3]{4^{3} a^{6} b^{7} c^{9}}$

Rewrite $a^{6}$ as ${(a^{2})}^{3}$ .

$\sqrt[3]{4^{3} {(a^{2})}^{3} b^{7} c^{9}}$

Factor out $b^{6}$ .

$\sqrt[3]{4^{3} {(a^{2})}^{3} (b^{6} b) c^{9}}$

Rewrite $b^{6}$ as ${(b^{2})}^{3}$ .

$\sqrt[3]{4^{3} {(a^{2})}^{3} ({(b^{2})}^{3} b) c^{9}}$

Rewrite $c^{9}$ as ${(c^{3})}^{3}$ .

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

Move $b$ .

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

Rewrite $4^{3} {(a^{2})}^{3} ({(b^{2})}^{3}) {(c^{3})}^{3}$ as ${(4 a^{2} b^{2} c^{3})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

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