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Math Help - How do I prove b^x * b^y = b ^ x + y on R?

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by pDeCrunch View Post
    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
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    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.
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