Simplify cube root of 8a^8b^5

$\sqrt[3]{8 a^{8} b^{5}}$

Step 1

Rewrite $8 a^{8} b^{5}$ as ${(2 a^{2} b)}^{3} (a^{2} b^{2})$ .

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

$\sqrt[3]{2^{3} a^{8} b^{5}}$

Factor out $a^{6}$ .

$\sqrt[3]{2^{3} (a^{6} a^{2}) b^{5}}$

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

$\sqrt[3]{2^{3} ({(a^{2})}^{3} a^{2}) b^{5}}$

Factor out $b^{3}$ .

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

Move $a^{2}$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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