# How do you simplify 100^(-1/2)?

Aug 26, 2016

$\frac{1}{100} ^ 0.5$

#### Explanation:

$\frac{1}{100} ^ 0.5 = \frac{1}{10}$

$= 0.1$

Aug 26, 2016

$\frac{1}{10}$

#### Explanation:

There are 2 different laws of indices being used here.

A negative index $\leftarrow \text{use the reciprocal}$
A fraction in the index $\leftarrow \text{ same as a root}$

It does not matter which law you apply first.
I prefer to get rid of the negative index first.

${100}^{- \frac{1}{2}} = \frac{1}{{100}^{\frac{1}{2}}}$

$\frac{1}{{100}^{\frac{1}{2}}} = \frac{1}{\sqrt{100}}$

=$\frac{1}{10}$