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Prove a^0 = 1 if a=/=0

  1. Feb 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that a^0 = 1 if a is not equal to 0.

    2. Relevant equations



    3. The attempt at a solution
    Well,since a is not equal to 0, I replace it with another number.

    (1^0)^0 = 1

    (6^0)^0 = 1

    ETC

    Is this enough to prove that a^0 = 1 if a is not equal to 0.Even thought its a basic and easy question...im doubting.

    Thx
     
  2. jcsd
  3. Feb 9, 2008 #2
    hhmmm any1?...
     
  4. Feb 9, 2008 #3

    Dick

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    You haven't 'proved' anything. You just wrote down some numbers. What's your definition of a^x? If it's e^(log(a)*x) the answer is pretty easy, just take the log of both sides. To prove something you need a precise definition of the thing you are trying to prove. What does a^x mean?
     
  5. Feb 10, 2008 #4

    Dick

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    Are you just assuming the laws of exponents? Like (a^n)*(a^m)=a^(n+m)? If so, then set m=0 and solve for a^m.
     
  6. Feb 10, 2008 #5
    Thanks, i though about doing that before, dunno what came up in mind.
     
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