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

1 Answer
Mar 19, 2016

Answer:

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#