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?