Algebra Examples

$\frac{1}{2 x \sqrt{y}}$

Step 1

Multiply $\frac{1}{2 x \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{1}{2 x \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{1}{2 x \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

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

Step 2.2

Move $\sqrt{y}$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

$\frac{\sqrt{y}}{2 x {\sqrt{y}}^{1 + 1}}$

Step 2.6

Add $1$ and $1$ .

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

Step 2.7

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

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Step 2.7.1

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

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

Step 2.7.2

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

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

Step 2.7.3

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

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

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

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

Step 2.7.4.2

Rewrite the expression.

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

Step 2.7.5

Simplify.

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