I'm doing #3. sovalpha is of length s and its a cycle, alpha=(a1 a2....aS). so alpha inverse=(aS...a2 a1).
And now its saying, alpha inverse=alpha^(S-1) Now maybe im misunderstanding, but for example lets use Beta is a cycle of length 5 so B=(b1 b2 b3 b4 b5), does this mean that the inverse of Beta is also equal to (b1 b2 b3 b4) ,since its 5-1=4?
No, one has order 5 the other has order 4, just because you raise something to a certain power doesn't mean you lose what things go to, if you look at the original permutation:
by definition this means skip
things and go to the next one, you should be able to see that this means the same thing as "go to the previous thing in the cycle listed" i.e. the inverse is
, since cycles are the same up to cyclic permutation.