Algebra Examples

$\frac{5 x y^{- 1}}{\sqrt{25 x y}}$

Step 1

Move $y^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 x}{\sqrt{25 x y} y}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25 x y$ as $5^{2} (x y)$ .

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Step 2.1.1

Rewrite $25$ as $5^{2}$ .

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

Step 2.1.2

Add parentheses.

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

Step 2.2

Pull terms out from under the radical.

$\frac{5 x}{5 \sqrt{x y} y}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 x}{5 \sqrt{x y} y}$

Step 3.2

Rewrite the expression.

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

Step 4

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

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

Step 5

Combine and simplify the denominator.

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Step 5.1

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

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

Step 5.2

Move $\sqrt{x y}$ .

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

Step 5.3

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

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

Step 5.4

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

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

Step 5.5

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

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

Step 5.6

Add $1$ and $1$ .

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

Step 5.7

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

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Step 5.7.1

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

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

Step 5.7.2

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

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

Step 5.7.3

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

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

Step 5.7.4

Cancel the common factor of $2$ .

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Step 5.7.4.1

Cancel the common factor.

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

Step 5.7.4.2

Rewrite the expression.

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

Step 5.7.5

Simplify.

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

Step 6

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

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Step 6.1

Move $y$ .

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

Step 6.2

Multiply $y$ by $y$ .

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

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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