How do you prove the following exponent laws for groups?
let x be an element of group G. Then for all integers m and n:
(i) x^-n = (x^-1)^n
(ii) x^m . x^n = x^(m+n)
(iii) x^m . x^n = x^n . x^m
(iv) (x^m)^n = x^(mn)
They seem self-evident, but I'm not quite sure how to prove them, especially when m and n are negative integers.