Simplify 3y cube root of 8x^3y^11

$3 y \sqrt[3]{8 x^{3} y^{11}}$

Step 1

Rewrite $8 x^{3} y^{11}$ as ${(2 x y^{3})}^{3} y^{2}$ .

Rewrite $8$ as $2^{3}$ .

$3 y \sqrt[3]{2^{3} x^{3} y^{11}}$

Factor out $y^{9}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

Multiply $y^{3}$ by $y$ .

Raise $y$ to the power of $1$ .

$3 (y^{3} y^{1}) (2 x \sqrt[3]{y^{2}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 y^{3 + 1} (2 x \sqrt[3]{y^{2}})$

Add $3$ and $1$ .

$3 y^{4} (2 x \sqrt[3]{y^{2}})$

Step 4

Multiply $2$ by $3$ .

$6 y^{4} (x \sqrt[3]{y^{2}})$

Step 5

Reorder factors in $6 y^{4} (x \sqrt[3]{y^{2}})$ .

$6 y^{4} x \sqrt[3]{y^{2}}$