Confusion with induction problem.

[Unassuming]

Homework Statement

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.

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

 

[HallsofIvy]

If you have proved that aⁿa_{m[/sup]= a^n+m for positive integers then you should be able to prove, in the same way, that a^-na^-m= a^-n-m for m and n any positive integers.}