# How do you simplify (3/2) ^ -4 * (3/2) ^ 2?

Mar 19, 2016

I found: $\frac{4}{9}$

#### Explanation:

We can use a property of the exponents to add them in case of a mutiplication of same base:

${\left(\frac{3}{2}\right)}^{-} 4 \cdot {\left(\frac{3}{2}\right)}^{2} = {\left(\frac{3}{2}\right)}^{\textcolor{red}{- 4 + 2}} = {\left(\frac{3}{2}\right)}^{-} 2 =$

We can now invert the fraction to get rid of the minus in the exponent:
$= {\left(\textcolor{b l u e}{\frac{2}{3}}\right)}^{2} =$
and:
${2}^{2} / {3}^{2} = \frac{4}{9}$