Direct Proofs (2)

Write clear and complete direct proofs for the following mathematical statement.
(2) If x | a and y | b, then a = xm and b = yn for some integers m and n. Then

                                       ab = (xm)(yn)
                                           = xy(mn)
                                           = (xy)q

where q = mn is an integer. Thus xy | ab as desired.

QED