Algebra Examples

$1 \sqrt{π n}$

Step 1

Multiply to rationalize the numerator.

$\frac{1 (\sqrt{π n} \sqrt{π n})}{\sqrt{π n}}$

Step 2

Simplify.

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Step 2.1

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

$\frac{1 ({\sqrt{π n}}^{1} \sqrt{π n})}{\sqrt{π n}}$

Step 2.2

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

$\frac{1 ({\sqrt{π n}}^{1} {\sqrt{π n}}^{1})}{\sqrt{π n}}$

Step 2.3

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

$\frac{1 {\sqrt{π n}}^{1 + 1}}{\sqrt{π n}}$

Step 2.4

Add $1$ and $1$ .

$\frac{1 {\sqrt{π n}}^{2}}{\sqrt{π n}}$

Step 2.5

Rewrite ${\sqrt{π n}}^{2}$ as $π n$ .

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Step 2.5.1

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

$\frac{1 {({(π n)}^{\frac{1}{2}})}^{2}}{\sqrt{π n}}$

Step 2.5.2

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

$\frac{1 {(π n)}^{\frac{1}{2} \cdot 2}}{\sqrt{π n}}$

Step 2.5.3

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

$\frac{1 {(π n)}^{\frac{2}{2}}}{\sqrt{π n}}$

Step 2.5.4

Cancel the common factor of $2$ .

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Step 2.5.4.1

Cancel the common factor.

$\frac{1 {(π n)}^{\frac{2}{2}}}{\sqrt{π n}}$

Step 2.5.4.2

Rewrite the expression.

$\frac{1 {(π n)}^{1}}{\sqrt{π n}}$

Step 2.5.5

Simplify.

$\frac{1 (π n)}{\sqrt{π n}}$