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Thread: Exponent problem!!

  1. #1
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    Exponent problem!!

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    Last edited by Revelsyn; Oct 13th 2008 at 07:18 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Revelsyn View Post
    I got a review of exponents sheet last math class and I can't figure out how to do this one ><; I've been given the answer but I don't understand the process; help anyone

    "Evaluate."

    2ľn(2n - 2+ n)

    ~ everything in red is an exponent
    ~the sheet says the answer is supposed to be -1
    $\displaystyle 2^{-n} \left ( 2^n - 2^{1 + n} \right )$

    First, note that multiplication is distributive over addition, so this is:
    $\displaystyle 2^{-n} \left ( 2^n - 2^{1 + n} \right ) = 2^{-n} \cdot 2^n - 2^{-n} \cdot 2^{1 + n}$

    Now use the property that
    $\displaystyle a^x \cdot a^y = a^{x + y}$

    So:
    $\displaystyle = 2^{-n + n} - 2^{-n + 1 + n} = 2^0 - 2^1$

    $\displaystyle = 1 - 2 = -1$

    -Dan
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  3. #3
    Math Engineering Student
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    Other way

    $\displaystyle 2^{-n}(2^n-2^{1+n})=2^{-n}\cdot2^n(1-2)=-1$

    Cheers,
    K.
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