Evaluate square root of 10^-8

$\sqrt{10^{- 8}}$

Step 1

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

$\sqrt{\frac{1}{10^{8}}}$

Step 2

Raise $10$ to the power of $8$ .

$\sqrt{\frac{1}{100000000}}$

Step 3

Rewrite $\sqrt{\frac{1}{100000000}}$ as $\frac{\sqrt{1}}{\sqrt{100000000}}$ .

$\frac{\sqrt{1}}{\sqrt{100000000}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{100000000}}$

Step 5

Simplify the denominator.

Rewrite $100000000$ as $10000^{2}$ .

$\frac{1}{\sqrt{10000^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{10000}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10000}$

Decimal Form:

$0.0001$