Assignment:
Let G be a group, let a, b be elements in G and let m and n be (not necessarily positive) integers.
Prove that:
i) (a^n)^m= (a^mn)
ii) if a and b commute, then (ab)^n = a^n times b^n
iii) a^m times a^n = (a)^(m+n)
Provide complete and step by step solution for the question and show calculations and use formulas.