# How do you simplify (9/2)^-1?

Jun 18, 2018

See a solution process below:

#### Explanation:

There are a couple of ways we can do this. The first is to use these two rules of exponents:

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

${\left(\frac{9}{2}\right)}^{\textcolor{red}{- 1}} \implies \frac{1}{\frac{9}{2}} ^ \textcolor{red}{- - 1} \implies \frac{1}{\frac{9}{2}} ^ \textcolor{red}{1} \implies \frac{1}{\frac{9}{2}} \implies \frac{2}{9}$

Another way is to use these rules of exponents:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$ and $\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$ and ${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$ and ${a}^{\textcolor{red}{1}} = a$

${\left(\frac{9}{2}\right)}^{\textcolor{red}{- 1}} \implies {9}^{\textcolor{red}{- 1}} / {2}^{\textcolor{red}{- 1}} \implies {9}^{\textcolor{red}{- 1}} \times \frac{1}{2} ^ \textcolor{red}{- 1} \implies \frac{1}{9} ^ \textcolor{red}{- - 1} \times {2}^{\textcolor{red}{- - 1}} \implies \frac{1}{9} ^ \textcolor{red}{1} \times {2}^{\textcolor{red}{1}} \implies \frac{1}{9} \times 2 \implies \frac{2}{9}$