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Exponent laws

  1. Jul 31, 2011 #1
    1. The problem statement, all variables and given/known data

    2^-4 + 2^-6
    _____________
    2^-3


    2. Relevant equations



    3. The attempt at a solution

    Ive tried several times, I do the reciprical of all numbers

    ie) 1/2^4 + 1/2 ^6
    ___________________
    2^3

    Which gives me The wrong answer, cause i do the addiition first, finish all the powers and cant get the right answer. The book shows the next step to be...

    2^2 + 1
    ________
    2^6

    Which i dont get
     
  2. jcsd
  3. Jul 31, 2011 #2

    eumyang

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    Don't rewrite the expression with positive exponents. (You did it wrong, anyway.) Instead, multiply the numerator and denominator by 26.
     
  4. Jul 31, 2011 #3
    wat..? Dont make them positive yet multiply them with a positive denom. ? I dont even understand how the person got to 2^6.
     
  5. Jul 31, 2011 #4

    eumyang

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    Homework Helper

    It would also be helpful if you can check your original problem for typos. Because the problem you state:
    [tex]\frac{2^{-4} + 2^{-6}}{2^{-3}}[/tex]
    does not equal the answer you state:
    [tex]\frac{2^{2} + 1}{2^{6}}[/tex]
    Sure, why not? If the original problem you stated was typed correctly, then I would multiply numerator by denominator by 26, because 2-6 is the smallest power of 2. 2-6 * 26 = 1, after all.

    If you look at this similar example:
    [tex]\frac{5^{-7} + 5^{-2}}{5^{-5}}[/tex]
    I would multiply top and bottom by 57 because 5-7 is the smallest power shown.
     
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