Prove a^(m+n) = a^m + a^n with mathematical induction

1. Jan 16, 2012

gluttony

prove by induction that, 1) a^(m+n) = a^m + a^n

2) (a^m)^n=a^(mn)

2. Relevant equations -- mathematical induction

3. The attempt at a solution
the equations hold for a = 1.
let's say the equation hold for a = s; then s^(m+n) = s^m + s^n
now for a = s+1; (s+1)^(m+n) = (binomial expansion of s+1)

how can i prove that (s+1)^(m+n) = (s+1)^m * (s+1)^n

2. Jan 16, 2012

D H

Staff Emeritus
You can't prove that because it's not true. 22+1=23=8, 22+21=4+2=6, and 8 is obviously not equal to 6.

What you can prove is that am^n = am*an.

Wrong approach. Try starting with n=0 as your base case rather than a=1. And of course you do want to prove the corrected thesis.