# How do you simplify (100^(1/2))^-4?

Jan 3, 2017

See full simplification process below

#### Explanation:

First step is to simplify the terms in the parenthesis:

${\left({100}^{\frac{1}{2}}\right)}^{-} 4 = {10}^{-} 4$

Next we can use this rule for exponents to further simplify:

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

Substituting gives:

${10}^{\textcolor{red}{- 4}} = \frac{1}{10} ^ \textcolor{red}{- - 4} = \frac{1}{10} ^ 4 = \frac{1}{10 \times 10 \times 10 \times 10} =$

$\frac{1}{10000}$ or $0.0001$