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Math Help - Exponential Problem

  1. #1
    Junior Member BobBali's Avatar
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    Exponential Problem

    Hi,
    Good day All,

    The problem asks to simplify without using a calculator:

    \frac{2^{14} - 2^{11} + 7}{2^{11} + 7}


    \frac{2^{11} (2^{3} - 1) + 7}{2^{11} + 1}


    \frac{2^{11} (8-1) + 7}{2^5  2^5  2^1}


    \frac{2^5 2^5 2^1 (7) +7}{2^5 2^5 2^1 + 1}


    Not sure if i'm on the right track....?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Exponential Problem

    I assume you mean:

    \frac{2^{14}-2^{11}+7}{2^{11}+1}=\frac{2^{11}(2^3-1)+7}{2^{11}+1}=\frac{7(2^{11}+1)}{2^{11}+1}=7
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  3. #3
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    Re: Exponential Problem

    Quote Originally Posted by MarkFL2 View Post
    I assume you mean:

    \frac{2^{14}-2^{11}+7}{2^{11}+1}=\frac{2^{11}(2^3-1)+7}{2^{11}+1}=\frac{7(2^{11}+1)}{2^{11}+1}=7

    sorry, I am not the one who posted this question but I am just curious...
    How did you get 7(2^11 +1)/ 2^11 +1 from 2^11(2^3 -1) +7 / 2^11 +1 ???
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Exponential Problem

    I will add an intermediary step:

    \frac{2^{14}-2^{11}+7}{2^{11}+1}=\frac{2^{11}(2^3-1)+7}{2^{11}+1}=\frac{2^{11}\cdot7+7}{2^{11}+1}= \frac{7(2^{11}+1)}{2^{11}+1}=7
    Thanks from puresoul and BobBali
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  5. #5
    Junior Member
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    Re: Exponential Problem

    Quote Originally Posted by MarkFL2 View Post
    I will add an intermediary step:

    \frac{2^{14}-2^{11}+7}{2^{11}+1}=\frac{2^{11}(2^3-1)+7}{2^{11}+1}=\frac{2^{11}\cdot7+7}{2^{11}+1}= \frac{7(2^{11}+1)}{2^{11}+1}=7
    Oh..
    I didn't realise that 2^3 -1 is 7
    Thnks ^^
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