# How do you simplify 100^(-3/2)?

Jan 3, 2017

See full explanation below:

#### Explanation:

First, we need to understand the following exponent rule:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

The reverse is also true:

${x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}} = {\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}}$

We can modify this expression as follows using these rules:

${100}^{- \frac{3}{2}} = {100}^{\textcolor{red}{\frac{1}{2}} \times \textcolor{b l u e}{- 3}} = {\left({100}^{\frac{1}{2}}\right)}^{-} 3$

We can now simplify the term within parenthesis:

${\left({100}^{\frac{1}{2}}\right)}^{-} 3 = {10}^{-} 3$

Next we need to understand this rule for exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

Applying this rule to our problem gives:

${10}^{\textcolor{red}{- 3}} = \frac{1}{10} ^ \textcolor{red}{- - 3} = \frac{1}{10} ^ \textcolor{red}{3} = \frac{1}{10 \times 10 \times 10} = \frac{1}{1000}$ or $0.001$