Hey CuriousChris.

The basic reason is that 3^2 = 9 and power laws work in that (x^a)^b = x^(ab) so if you let x = 3 a = 2 and b = x+1 then (3^2)^(x+1) = 3^(2(x+1)) = 3^(2x+1) = 9^(x+1).

So if 3^(2x+2)/3^(2x-1) using exponent laws if you divide you subtract the bottom index from the top to get 3^(2x+2 - (2x-1)) = 3^(2+1) = 3^3.