Simplify cube root of 24a^6b^5

$\sqrt[3]{24 a^{6} b^{5}}$

Step 1

Rewrite $24 a^{6} b^{5}$ as ${(2 a^{2} b)}^{3} \cdot (3 b^{2})$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) a^{6} b^{5}}$

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

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

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

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

Factor out $b^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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