Simplify cube root of 54xy^5

$\sqrt[3]{54 x y^{5}}$

Step 1

Rewrite $54 x y^{5}$ as ${(3 y)}^{3} \cdot (2 x y^{2})$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x y^{5}}$

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

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

Factor out $y^{3}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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