Basic Math Examples

$\frac{3}{\sqrt{9 a}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{3}{\sqrt{3^{2} a}}$

Step 1.2

Pull terms out from under the radical.

$\frac{3}{3 \sqrt{a}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3}{3 \sqrt{a}}$

Step 2.2

Rewrite the expression.

$\frac{1}{\sqrt{a}}$

Step 3

Multiply $\frac{1}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{1}{\sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{1}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{\sqrt{a}}{\sqrt{a} \sqrt{a}}$

Step 4.2

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

$\frac{\sqrt{a}}{{\sqrt{a}}^{1} \sqrt{a}}$

Step 4.3

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

$\frac{\sqrt{a}}{{\sqrt{a}}^{1} {\sqrt{a}}^{1}}$

Step 4.4

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

$\frac{\sqrt{a}}{{\sqrt{a}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{a}}{{\sqrt{a}}^{2}}$

Step 4.6

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

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Step 4.6.1

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

$\frac{\sqrt{a}}{{(a^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{\sqrt{a}}{a^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{\sqrt{a}}{a^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{a}}{a^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{a}}{a^{1}}$

Step 4.6.5

Simplify.

$\frac{\sqrt{a}}{a}$