I tried to do this a different way where while dealing with the exponents in the 2nd bracket i put everything over 1 (since the exponent is -1) therefore making that second bracket [1/ (x^1/2y^-3/4)] i changed the 1/2 power from negative to positive and the 3/4 power from postive to negative after that i just multiplied across with exponents like this:

[ (x^-3/2y^1) / (x^1/2y^-2) ] TIMES [ 1 / (x^1/2y^-3/4)]

= (x^-3/2y) / (xy^-11/4)

= x^-5/2y^15/4

SO NOW, when i do it this way i get the correct exponent values for the y and incorrect for the x.. but in the step before the x is the correct value.

Ugh. I really do not understand what I am doing wrong and am about to give up on this question.