(x-3/2)^3 multiplied by (1/x-3)^2?

(x-3/2)^3(1/x-3)^2
=[(x^3+3x^2(-3/2)+3x(-3/2)^2
+(-3/2)^3](1/x^2-6/x+9)
To simplify it further, use the distributive law of multiplication.
You may try it yourself.

Do you mean :-

[ (x - 3) / 2 ]³
----------------
(x - 3)²

(x - 3) / 8

Question is unclear due to lack of brackets I`m afraid.

=(x^3-9 x^2/2+27 x/4-27/8)*(9-6/x+1/x^2)
=9 x^3-93 x^2/2+355 x/4-603/8+27/x-27/(8 x^2)

((x-3)/2) ^3 really equals ((x-3)^3)/8

(1/(x-3))^2 really equals 1/((x-3)^2)

Thus the two quantities multiplied by each other yields
(x-3)/8

[(x - 3)/2]^3 * [1/(x - 3)]^2
= [(x - 3)^3/8][1/(x - 3)^2]
= [(x - 3)^3 * 1]/[8 * (x - 3)^2]
= (x - 3)^3/8(x - 3)^2 [divide (x - 3)^2 and (x - 3)^3 by (x - 3)^2]
= (x - 3)/8