Simplify 2y cube root of 135x^6y^3

$2 y \sqrt[3]{135 x^{6} y^{3}}$

Step 1

Rewrite $135 x^{6} y^{3}$ as ${(3 x^{2} y)}^{3} \cdot 5$ .

Factor $27$ out of $135$ .

$2 y \sqrt[3]{27 (5) x^{6} y^{3}}$

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

$2 y \sqrt[3]{3^{3} \cdot 5 x^{6} y^{3}}$

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

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

Move $5$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 4

Multiply $3$ by $2$ .

$6 y^{2} x^{2} \sqrt[3]{5}$