Simplify cube root of 81y^6

$\sqrt[3]{81 y^{6}}$

Step 1

Rewrite $81 y^{6}$ as ${(3 y^{2})}^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) y^{6}}$

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

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

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

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

Move $3$ .

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

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

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

Step 2

Pull terms out from under the radical.

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