Simplify cube root of 108x^3y^5

$\sqrt[3]{108 x^{3} y^{5}}$

Step 1

Rewrite $108 x^{3} y^{5}$ as ${(3 x y)}^{3} \cdot (4 y^{2})$ .

Factor $27$ out of $108$ .

$\sqrt[3]{27 (4) x^{3} y^{5}}$

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

$\sqrt[3]{3^{3} \cdot 4 x^{3} y^{5}}$

Factor out $y^{3}$ .

$\sqrt[3]{3^{3} \cdot 4 x^{3} (y^{3} y^{2})}$

Move $4$ .

$\sqrt[3]{3^{3} x^{3} y^{3} \cdot 4 y^{2}}$

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

$\sqrt[3]{{(3 x y)}^{3} \cdot 4 y^{2}}$

Add parentheses.

$\sqrt[3]{{(3 x y)}^{3} \cdot (4 y^{2})}$

Step 2

Pull terms out from under the radical.

$3 x y \sqrt[3]{4 y^{2}}$