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Homework Help: Exponent expression help

  1. Jun 29, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]0^{\sqrt{0}}=\sqrt{0^{0}}[/tex]

    Is this expression true?
     
  2. jcsd
  3. Jun 29, 2008 #2

    CompuChip

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    Re: Exponent

    If you consider "undefined = undefined" to be true, then yes.
     
  4. Jun 29, 2008 #3
    Re: Exponent

    That depends on your view... 0^0 can be defined as 1, or it can be undefined.

    See http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power


    Either way, I think if you define 0^0 as undefined then the expression above does not hold... That would also mean 1/0 = 0^0 which I think doesn't really make sense... I'm not sure on this but I don't think you can say undefined = undefined!
     
  5. Jun 29, 2008 #4
    Re: Exponent

    Take logarithm and simplify.

    root 0 * log 0 = 0 *1= 0

    Assumptions= using root 0= 0 on the basis that zero is a real number.
    Taking log to the base 10.

    R.H.S.> 1/2*0 * log 0
    > 0*1
    > 0

    Assumptions same as above.

    The points raised above by honourable members are very meaningful, this is one of the proof methods i learned at the IIT,delhi.
     
  6. Jun 29, 2008 #5

    HallsofIvy

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    Re: Exponent

    ?? log(0) is NOT 1. It is, one more time, "undefined".
    (log(1)= 0, not the other way around.)

     
  7. Jun 30, 2008 #6
    Re: Exponent

    It was a bad typing error.
     
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