1. The problem statement, all variables and given/known data Prove that if 0≤x<y then xn < yn 2. Relevant equations 12 properties of numbers. 3. The attempt at a solution For the case: 0 =x < y is trivial. So now we just need y > x > 0 : Now, I am having a bit of trouble with this. Take the case where n=2: x < y so x*x < x*y AND x*y < y*y and so by transitivity x*x < y*y. But when I upgrade to being arbitrary: x < y x*xa < y*xa AND x*ya < y*ya but I cannot make the connection by transitivity. Is there a completely different approach for this that I am overlooking?