Simplify cube root of 24a^10b^6

$\sqrt[3]{24 a^{10} b^{6}}$

Step 1

Rewrite $24 a^{10} b^{6}$ as ${(2 a^{3} b^{2})}^{3} \cdot (3 a)$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) a^{10} b^{6}}$

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

$\sqrt[3]{2^{3} \cdot 3 a^{10} b^{6}}$

Factor out $a^{9}$ .

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

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

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

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

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

Move $a$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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