# Thread: How do I prove b^x * b^y = b ^ x + y on R?

1. ## How do I prove b^x * b^y = b ^ x + y on R?

How do I prove b^x * b^y = b ^ x + y where b > 1 and x, y are on R?

2. Originally Posted by pDeCrunch
How do I prove b^x * b^y = b ^ x + y where b > 1 and x, y are on R?
Look at how $b^x$ is defined for $x \in \mathbb{R}$, you will find it is defined as a limit of rational powers. Now look at how you might define $b^x b^y$.

CB

3. Originally Posted by CaptainBlack
Look at how $b^x$ is defined for $x \in \mathbb{R}$, you will find it is defined as a limit of rational powers. Now look at how you might define $b^x b^y$.

CB
Is it sufficient to say that x <= a, y <= b (supremum) then x + y <= a + b
so b ^ x + y <= b ^ a + b, how do I proceed to make the >= argument so that I can wedge them and make an equivalence relation.