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.