Simplify y^2 cube root of 16x^11y^10

$y^{2} \sqrt[3]{16 x^{11} y^{10}}$

Step 1

Rewrite $16 x^{11} y^{10}$ as ${(2 x^{3} y^{3})}^{3} \cdot (2 x^{2} y)$ .

Factor $8$ out of $16$ .

$y^{2} \sqrt[3]{8 (2) x^{11} y^{10}}$

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

$y^{2} \sqrt[3]{2^{3} \cdot 2 x^{11} y^{10}}$

Factor out $x^{9}$ .

$y^{2} \sqrt[3]{2^{3} \cdot 2 (x^{9} x^{2}) y^{10}}$

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

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

Factor out $y^{9}$ .

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

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

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

Move $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

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

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