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

• Oct 24th 2008, 11:36 PM
pDeCrunch
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?
• Oct 25th 2008, 12:03 AM
CaptainBlack
Quote:

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 $\displaystyle b^x$ 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
• Oct 25th 2008, 12:15 AM
pDeCrunch
Quote:

Originally Posted by CaptainBlack
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.