a^3 x b^2 = ????

Well...I don't think you can really simplify this further because the bases are different and the exponents are different.

Correct me if I'm wrong (I'm terrible at defining and explaining...). 

You can factor out in a few ways,if that is the question

realise that a^3 X b^2    =  a x a x a x b x b       so you can have 

                                      = a(a x a x b xb)    = a(a^2b^2)       

or a^2(a x b^2)     etc   etc    .     But in most calculations, a^3b^2 is probably the simplest form.