Simplify ( square root of x^5y^3)/(x^2y^3)

$\frac{\sqrt{x^{5} y^{3}}}{x^{2} y^{3}}$

Simplify the numerator.

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

Factor out $x^{4}$ .

$\frac{\sqrt{x^{4} x y^{3}}}{x^{2} y^{3}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Factor out $y^{2}$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$\frac{x^{2} y \sqrt{x y}}{x^{2} y^{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} y \sqrt{x y}}{x^{2} y^{3}}$

Rewrite the expression.

$\frac{y \sqrt{x y}}{y^{3}}$

Cancel the common factor of $y$ and $y^{3}$ .

Factor $y$ out of $y \sqrt{x y}$ .

$\frac{y (\sqrt{x y})}{y^{3}}$

Cancel the common factors.

Factor $y$ out of $y^{3}$ .

$\frac{y (\sqrt{x y})}{y \cdot y^{2}}$

Cancel the common factor.

$\frac{y \sqrt{x y}}{y \cdot y^{2}}$

Rewrite the expression.

$\frac{\sqrt{x y}}{y^{2}}$