Question

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

Answer 1

I found: `4/9`

Explanation:

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

`(3/2)^-4*(3/2)^2=(3/2)^(color(red)(-4+2))=(3/2)^-2=`

We can now invert the fraction to get rid of the minus in the exponent:
`=(color(blue)(2/3))^2=`
and:
`2^2/3^2=4/9`