1. Limited time only! Sign up for a free 30min personal 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!

Proof of adding powers (real analysis)

  1. Oct 1, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove that br+s=brbs if r and s are rational.

    2. Relevant equations

    So far we know the basic field axioms and a a few other things related to powers.
    1.) For every real x>0 and every integer n>0 there is one and only one positive real y such that yn=x
    2.) if a and b are positive real numbers and n is a positive integer, then (ab)1/n=a1/nb1/n
    3.)(ba)b=bab

    3. The attempt at a solution

    When I look at this problem I don't see any way to use the three facts above. The first thing that jumps at me is the field axiom of multiplicative associativity. So for me I see the proof as going as such.

    Asssume r and s are rational. br+s=brbs due to multiplicative associativity. (QED)


    Is the proof this simple or am I missing something?
     
    Last edited: Oct 1, 2011
  2. jcsd
  3. Oct 3, 2011 #2
    Any help would be appreciated.
     
  4. Oct 4, 2011 #3

    Mark44

    Staff: Mentor

    How can you represent a rational number r?
     
  5. Oct 4, 2011 #4
    I could say that r=m/n, s=u/v where m,n,u, and v are all integers and both n and v are not equal to zero. From here I still have the same problem though. I don't have any ideas for any inbetween steps. All I see is a simple regrouping ( associativity). Is there more to than that or is it really this simple?
     
  6. Oct 4, 2011 #5

    Mark44

    Staff: Mentor

    OK, that's a start.

    The right side of the equation you're trying to prove is brbs. Use the representations above of r and s, and #2 and #3 in your list of relevant equations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof of adding powers (real analysis)
  1. Real Analysis Proof (Replies: 7)

Loading...