Simplify cube root of 54y^10

$\sqrt[3]{54 y^{10}}$

Step 1

Rewrite $54 y^{10}$ as ${(3 y^{3})}^{3} \cdot (2 y)$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) y^{10}}$

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

$\sqrt[3]{3^{3} \cdot 2 y^{10}}$

Factor out $y^{9}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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