Simplify cube root of 72x^5y^9

$\sqrt[3]{72 x^{5} y^{9}}$

Step 1

Rewrite $72 x^{5} y^{9}$ as ${(2 x y^{3})}^{3} \cdot (9 x^{2})$ .

Factor $8$ out of $72$ .

$\sqrt[3]{8 (9) x^{5} y^{9}}$

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

$\sqrt[3]{2^{3} \cdot 9 x^{5} y^{9}}$

Factor out $x^{3}$ .

$\sqrt[3]{2^{3} \cdot 9 (x^{3} x^{2}) y^{9}}$

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

$\sqrt[3]{2^{3} \cdot 9 (x^{3} x^{2}) {(y^{3})}^{3}}$

Move $x^{2}$ .

$\sqrt[3]{2^{3} \cdot 9 (x^{3}) {(y^{3})}^{3} x^{2}}$

Move $9$ .

$\sqrt[3]{2^{3} (x^{3}) {(y^{3})}^{3} \cdot 9 x^{2}}$

Rewrite $(2^{3} (x^{3})) {(y^{3})}^{3}$ as ${(2 x y^{3})}^{3}$ .

$\sqrt[3]{{(2 x y^{3})}^{3} \cdot 9 x^{2}}$

Add parentheses.

$\sqrt[3]{{(2 x y^{3})}^{3} \cdot (9 x^{2})}$

Step 2

Pull terms out from under the radical.

$2 x y^{3} \sqrt[3]{9 x^{2}}$