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(x^y)*(y^(-x))=1 is very rare for integers...
it can happen only if x^y=y^x

there are only few integer solutions to that:
(2,4),(4,2),(-2,-4),(-4,-2) and (a,a) for every integer a not equals to 0.

just check to see that none of the options satisfy st2. which means that if st2 is true - x and y are not one of these, and the answer to stem question is no. hence sufficient.
st1, however, can accomodate some of the solutions (and of course accomodate more different combinations). hence insufficient.