PowerSimplify[exp]
simplifies (-x)^a
to (-1)^a x^a
and (y-x)^n
to (-1)^n (x-y)^n
thus assuming that the exponent is an integer (even if it is symbolic).
Furthermore, (-1)^(a+n)
and I^(a+n)
are expanded and (I)^(2 m) -> (-1)^m and (-1)^(n_Integer?EvenQ m) -> 1
and (-1)^(n_Integer?OddQ m) -> (-1)^m
for n
even and odd respectively and (-1)^(-n) -> (-1)^n
and Exp[I m Pi] -> (-1)^m
.
[(-1)^(2 OPEm)] PowerSimplify
[(-1)^(OPEm + 2)] PowerSimplify
[(-1)^(OPEm - 2)] PowerSimplify
[I^(2 OPEm)] PowerSimplify