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Prime factorization, Exponents

  1. Mar 25, 2007 #1
    This was taken from a math contest a few months ago.
    1. The problem statement, all variables and given/known data

    find z if:
    x=28 * 38
    y=212 * 36

    2. Relevant equations
    Theres undoubtably some trick, but I have yet to find it

    3. The attempt at a solution
    Dont even think about calculator

    I showed my math teacher, and he was able to find that zz=2(211*37*11) * 3(211*37*7)

    or 249268736 * 331352832

    How do you get z alone?
  2. jcsd
  3. Mar 25, 2007 #2
    [tex]z^{z} = 2^{2^{11}*3^{7}*11} * 3^{2^{11}*3^{7}*7} = ({2^{11}})^{2^{11}*3^{7}}*({3^{7}})^{2^{11}*3^{7}} = ({2^{11}*3^{7}})^{2^{11}*3^{7}} [/tex]

    [tex]z = {2^{11}*3^{7}} [/tex]
    Last edited: Mar 25, 2007
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