Simplify y^2 cube root of 8x^8y^3

$y^{2} \sqrt[3]{8 x^{8} y^{3}}$

Step 1

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

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

$y^{2} \sqrt[3]{2^{3} x^{8} y^{3}}$

Factor out $x^{6}$ .

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

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

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

Move $x^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $y$ .

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

Multiply $y$ by $y^{2}$ .

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

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

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

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

Add $1$ and $2$ .

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

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