# How do you simplify square root of 10^-6?

Sep 13, 2015

You can write it as ${10}^{-} 3$ or $\frac{1}{1000}$

#### Explanation:

Square root of a number $a$ is the same as ${a}^{\frac{1}{2}}$, so you can write this number as:

${\left({10}^{- 6}\right)}^{\frac{1}{2}}$

If you have a number raised two a power twice, you can write it as one power, where the exponents are multiplied:

${\left({10}^{- 6}\right)}^{\frac{1}{2}} = {10}^{- 6 \cdot \left(\frac{1}{2}\right)} = {10}^{- 3}$

Finally if you would like to get rid of the exponent you have to remember that negative exponent can be rewritten as an inverse number, so you have:

${10}^{- 3} = \frac{1}{10} ^ 3 = \frac{1}{1000}$