Simplify 121/( square root of 11x^2y)

$\frac{121}{\sqrt{11 x^{2} y}}$

Step 1

Simplify the denominator.

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

Reorder $11$ and $x^{2}$ .

$\frac{121}{\sqrt{x^{2} \cdot 11 y}}$

Add parentheses.

$\frac{121}{\sqrt{x^{2} \cdot (11 y)}}$

Pull terms out from under the radical.

$\frac{121}{x \sqrt{11 y}}$

Step 2

Multiply $\frac{121}{x \sqrt{11 y}}$ by $\frac{\sqrt{11 y}}{\sqrt{11 y}}$ .

$\frac{121}{x \sqrt{11 y}} \cdot \frac{\sqrt{11 y}}{\sqrt{11 y}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{121}{x \sqrt{11 y}}$ by $\frac{\sqrt{11 y}}{\sqrt{11 y}}$ .

$\frac{121 \sqrt{11 y}}{x \sqrt{11 y} \sqrt{11 y}}$

Move $\sqrt{11 y}$ .

$\frac{121 \sqrt{11 y}}{x (\sqrt{11 y} \sqrt{11 y})}$

Raise $\sqrt{11 y}$ to the power of $1$ .

$\frac{121 \sqrt{11 y}}{x ({\sqrt{11 y}}^{1} \sqrt{11 y})}$

Raise $\sqrt{11 y}$ to the power of $1$ .

$\frac{121 \sqrt{11 y}}{x ({\sqrt{11 y}}^{1} {\sqrt{11 y}}^{1})}$

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

$\frac{121 \sqrt{11 y}}{x {\sqrt{11 y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{121 \sqrt{11 y}}{x {\sqrt{11 y}}^{2}}$

Rewrite ${\sqrt{11 y}}^{2}$ as $11 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11 y}$ as ${(11 y)}^{\frac{1}{2}}$ .

$\frac{121 \sqrt{11 y}}{x {({(11 y)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{121 \sqrt{11 y}}{x {(11 y)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{121 \sqrt{11 y}}{x {(11 y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{121 \sqrt{11 y}}{x {(11 y)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{121 \sqrt{11 y}}{x {(11 y)}^{1}}$

Simplify.

$\frac{121 \sqrt{11 y}}{x (11 y)}$

Step 4

Cancel the common factor of $121$ and $11$ .

Factor $11$ out of $121 \sqrt{11 y}$ .

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

Cancel the common factors.

Factor $11$ out of $x (11 y)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Simplify 121/( square root of 11x^2y)

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