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Math Help - simplifying exponents

  1. #1
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    simplifying exponents

    Right now in school we are covering limits but also doing a review. I have to simplify some exponents and got all of them on the assingment except two problems. They both involve exponents with different bases. The problems are

    10^2x 2^10x

    and

    3^x + 4^x / 5^x

    How would I go in approaching to solve these problems?

    Also I am not sure if I simplified a problem enogh

    The problem is

    (1/8)^-pi/3

    and I simplified it to 8^-pi/3.

    Is there a way to simplify this answer further.
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  2. #2
    o_O
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    #1: 10^{2x} \cdot 2^{10x}

    Use the fact that: a^cb^c = (ab)^c (Imagine c = x)

    #2: \frac{3^x + 4^x}{5^x}

    Not much to do here ...

    #3: \left(\frac{1}{8}\right)^{-\frac{\pi}{3}} = 8^{{\color{red}+}\frac{\pi}{3}} (No negative sign)

    Not much to do here either.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by o_O View Post
    #3: \left(\frac{1}{8}\right)^{-\frac{\pi}{3}} = 8^{{\color{red}+}\frac{\pi}{3}} (No negative sign)

    Not much to do here either.
    You could go the extra step and see that 8^{\frac{1}{3}}=2, so it could be simplified to 2^{\pi}.

    --Chris
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