1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Suggestions on how to go about proving a^(m+n)=a^(m)a^(n)

  1. Jul 14, 2013 #1
    Let a be a nonzero number and m and n be integers. Prove the following equality. a^(m+n)=a^(m)a^(n)


    Im not really sure what direction to go in. Im not sure if I need to show for n positive and negative separately or is there an easier way.


    My attempt/ideas:
    When n>0: a^(m)a^(n)= (a*a*...*a)(m times) *(a*a*a*a*...*a)(n times)
    =a*a*...*a(m+n times)
    =a^(m+n)
    When n<0: a^(m)a^(n)=a^(m)=a....a(m times)/ a...a(n times)
     
  2. jcsd
  3. Jul 14, 2013 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Are you familiar with induction?
     
  4. Jul 14, 2013 #3
    Yes we just went over it but i wasn't sure how to go about induction with m and n being integers...
     
  5. Jul 14, 2013 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    1) Take ##m=0##. Prove that ##a^{m + n} = a^m a^n##. This shouldn't be a problem.

    2) Assume the result holds for ##m##. Prove it holds for ##m+1##. So you know that ##a^{m+n} = a^m a^n##. You need to prove ##a^{m + n + 1} = a^{m+1} a^n##.
     
  6. Jul 14, 2013 #5
    So would you be able to say: Since a^(m+n)=a^(m)a^(n).
    Then this implies that: a^(m+n+1)= a^(m+1+n)= a^(m+1)a^(n)?

    This doesn't seem right because we are assuming what we are trying to prove.
    Why are you allowed to show for m+1 but dont have to for n+1 or do you just assume since m+1 works then n+1 works?
    Im still confused how this deals with the negative values of m and n.
     
  7. Jul 14, 2013 #6

    Zondrina

    User Avatar
    Homework Helper

    Hint :

    ##a^{m+n+1} = aaaa.....a##

    (m+n) + 1 times.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted