Simplify cube root of 81x^9y^4

$\sqrt[3]{81 x^{9} y^{4}}$

Step 1

Rewrite $81 x^{9} y^{4}$ as ${(3 x^{3} y)}^{3} \cdot (3 y)$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) x^{9} y^{4}}$

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

$\sqrt[3]{3^{3} \cdot 3 x^{9} y^{4}}$

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

$\sqrt[3]{3^{3} \cdot 3 {(x^{3})}^{3} y^{4}}$

Factor out $y^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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