Simplify ( square root of x^9y^11)/( square root of xy)

$\frac{\sqrt{x^{9} y^{11}}}{\sqrt{x y}}$

Step 1

Combine $\sqrt{x^{9} y^{11}}$ and $\sqrt{x y}$ into a single radical.

$\sqrt{\frac{x^{9} y^{11}}{x y}}$

Step 2

Reduce the expression $\frac{x^{9} y^{11}}{x y}$ by cancelling the common factors.

Factor $x$ out of $x^{9} y^{11}$ .

$\sqrt{\frac{x (x^{8} y^{11})}{x y}}$

Factor $x$ out of $x y$ .

$\sqrt{\frac{x (x^{8} y^{11})}{x (y)}}$

Cancel the common factor.

$\sqrt{\frac{x (x^{8} y^{11})}{x y}}$

Rewrite the expression.

$\sqrt{\frac{x^{8} y^{11}}{y}}$

Step 3

Cancel the common factor of $y^{11}$ and $y$ .

Factor $y$ out of $x^{8} y^{11}$ .

$\sqrt{\frac{y (x^{8} y^{10})}{y}}$

Cancel the common factors.

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

$\sqrt{\frac{y (x^{8} y^{10})}{y^{1}}}$

Factor $y$ out of $y^{1}$ .

$\sqrt{\frac{y (x^{8} y^{10})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (x^{8} y^{10})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{x^{8} y^{10}}{1}}$

Divide $x^{8} y^{10}$ by $1$ .

$\sqrt{x^{8} y^{10}}$

Step 4

Rewrite $x^{8} y^{10}$ as ${(x^{4} y^{5})}^{2}$ .

$\sqrt{{(x^{4} y^{5})}^{2}}$

Step 5

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

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