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