Let me spell out why. The approach taken for n=2 can be equally applied here. That is:

(n^(1/n))^n=n

This makes it obvious that it works for ALL n.

Above I said that the only negative number it worked with was -1. I incorrectly based that on the inability of my Excel sheet program to handle negative numbers. The algerba says otherwise:

(1/(1/((-n)^(1/n)))^n=(-n)^1=-n