Simplify x^2y cube root of 125x^6y^3

$x^{2} y \sqrt[3]{125 x^{6} y^{3}}$

Step 1

Rewrite $125 x^{6} y^{3}$ as ${(5 x^{2} y)}^{3}$ .

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

Step 2

Pull terms out from under the radical, assuming real numbers.

$x^{2} y (5 x^{2} y)$

Step 3

Rewrite using the commutative property of multiplication.

$5 x^{2} y (x^{2} y)$

Step 4

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

Move $x^{2}$ .

$5 (x^{2} x^{2}) y \cdot y$

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

$5 x^{2 + 2} y \cdot y$

Add $2$ and $2$ .

$5 x^{4} y \cdot y$

Step 5

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

Move $y$ .

$5 x^{4} (y \cdot y)$

Multiply $y$ by $y$ .

$5 x^{4} y^{2}$