Simplify the Radical Expression 5a cube root of 152a^4b^5

$5 a \sqrt[3]{152 a^{4} b^{5}}$

Rewrite $152 a^{4} b^{5}$ as ${(2 a b)}^{3} \cdot (19 a b^{2})$ .

Factor $8$ out of $152$ .

$5 a \sqrt[3]{8 (19) a^{4} b^{5}}$

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

$5 a \sqrt[3]{2^{3} \cdot 19 a^{4} b^{5}}$

Factor out $a^{3}$ .

$5 a \sqrt[3]{2^{3} \cdot 19 (a^{3} a) b^{5}}$

Factor out $b^{3}$ .

$5 a \sqrt[3]{2^{3} \cdot 19 (a^{3} a) (b^{3} b^{2})}$

Move $a$ .

$5 a \sqrt[3]{2^{3} \cdot 19 (a^{3}) b^{3} a b^{2}}$

Move $19$ .

$5 a \sqrt[3]{(2^{3} (a^{3})) b^{3} \cdot 19 a b^{2}}$

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

$5 a \sqrt[3]{{(2 a b)}^{3} \cdot 19 a b^{2}}$

Add parentheses.

$5 a \sqrt[3]{{(2 a b)}^{3} \cdot 19 (a b^{2})}$

Add parentheses.

$5 a \sqrt[3]{{(2 a b)}^{3} \cdot (19 a b^{2})}$

Pull terms out from under the radical.

$5 a (2 a b \sqrt[3]{19 a b^{2}})$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 (a \cdot a) (2 b \sqrt[3]{19 a b^{2}})$

Multiply $a$ by $a$ .

$5 a^{2} (2 b \sqrt[3]{19 a b^{2}})$

Multiply $2$ by $5$ .

$10 a^{2} (b \sqrt[3]{19 a b^{2}})$

Reorder factors in $10 a^{2} (b \sqrt[3]{19 a b^{2}})$ .

$10 a^{2} b \sqrt[3]{19 a b^{2}}$