Basic Math Examples

$\frac{\sqrt{5 a^{- 2}}}{10 a^{- 1}}$

Step 1

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

$\frac{\sqrt{5 a^{- 2}} a}{10}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\sqrt{5 \frac{1}{a^{2}}} a}{10}$

Step 2.2

Combine $5$ and $\frac{1}{a^{2}}$ .

$\frac{\sqrt{\frac{5}{a^{2}}} a}{10}$

Step 2.3

Rewrite $\frac{5}{a^{2}}$ as ${(\frac{1}{a})}^{2} \cdot 5$ .

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Step 2.3.1

Factor the perfect power $1^{2}$ out of $5$ .

$\frac{\sqrt{\frac{1^{2} \cdot 5}{a^{2}}} a}{10}$

Step 2.3.2

Factor the perfect power $a^{2}$ out of $a^{2}$ .

$\frac{\sqrt{\frac{1^{2} \cdot 5}{a^{2} \cdot 1}} a}{10}$

Step 2.3.3

Rearrange the fraction $\frac{1^{2} \cdot 5}{a^{2} \cdot 1}$ .

$\frac{\sqrt{{(\frac{1}{a})}^{2} \cdot 5} a}{10}$

Step 2.4

Pull terms out from under the radical.

$\frac{\frac{1}{a} \sqrt{5} a}{10}$

Step 2.5

Combine $\frac{1}{a}$ and $\sqrt{5}$ .

$\frac{\frac{\sqrt{5}}{a} a}{10}$

Step 3

Combine $\frac{\sqrt{5}}{a}$ and $a$ .

$\frac{\frac{\sqrt{5} a}{a}}{10}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{\sqrt{5} a}{a}$ by cancelling the common factors.

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Step 4.1.1

Cancel the common factor.

$\frac{\frac{\sqrt{5} a}{a}}{10}$

Step 4.1.2

Rewrite the expression.

$\frac{\frac{\sqrt{5}}{1}}{10}$

Step 4.2

Divide $\sqrt{5}$ by $1$ .

$\frac{\sqrt{5}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5}}{10}$

Decimal Form:

$0.22360679 \dots$