Simplify cube root of 27a^3b^7

$\sqrt[3]{27 a^{3} b^{7}}$

Step 1

Rewrite $27 a^{3} b^{7}$ as ${(3 a b^{2})}^{3} b$ .

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

$\sqrt[3]{3^{3} a^{3} b^{7}}$

Factor out $b^{6}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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