Simplify cube root of 81y^8

$\sqrt[3]{81 y^{8}}$

Step 1

Rewrite $81 y^{8}$ as ${(3 y^{2})}^{3} \cdot (3 y^{2})$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) y^{8}}$

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

$\sqrt[3]{3^{3} \cdot 3 y^{8}}$

Factor out $y^{6}$ .

$\sqrt[3]{3^{3} \cdot 3 (y^{6} y^{2})}$

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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