(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let a in R and a != 0. Define a^0=1 and for all n in the positive integers, a^-n = 1/a^n.

Show,

a^n a^m =a^(n+m)

(a^n)^m = a^nm

a^m b^m =(ab)^m

for all a,b != 0 and n,m in Z.

3. The attempt at a solution

Notice that last part where it says Z, not just N. I just proved these 3 laws using induction for n,m in N. I am confused now on how to approach the problem.

Do I fix n, and let m = -1 for the base case. Then assume the statement is true to m<0 and show it is also true for m-1 ?

Thank you for your time.

EDIT: P35 in Munkres, Topology

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# Homework Help: Confusion with induction problem.

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