Hmmm, this not only assumes that x is real but its also only one out of an infinite number of "solutions" for (x^i)^i.
In the complex domain we run into ambiguities quite often and easy and rules for calculating with powers etc. not always apply the same way as in domain real. That was the fine thing with MC11 and Maple - it defaults to domain real and most of the time simplified expressions the same way we would do (using some implicit assumptions).
The current Mathcad's muPad can't even simplify (2^i)^i to 1/2 wheras the numerics has no problem
muPad obviously thinks more complex (pun intended):
and so we have multiple ways to express (x^i)^i and Mathcad can't simplify to the one with k=0. I'd wish that MC would at least give the simplification similar to my expression. Mathcad will usually do so with "solve,fully" but in this case with no success
We can "verify" the multiple "solutions" with the numerics (the symbolics again is of no help, possibly again as of other ambiguities)
Just noticed that also Mathcads numerics does NOT simplify that expression to 1/x. Thats the reason for the strange lookin plots with all its jumps
What motivates these questions of yours?
Yes, this would also be of interest to me. Loi Le is around here for some years with his special questions and I also asked few times about the reason or the source of his various problems but unfortunately never got an answer.