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Why is (n^0=1)? where n is any positive number

  1. Jun 16, 2006 #1
    I just can't justify this in my simple mind. I just always accepted it because I was told that it is equal to 1 throughout highschool, and now in cegep. :confused:
     
  2. jcsd
  3. Jun 16, 2006 #2
    For an integer a:

    n^0 = n^(a-a) = n^a(n^-a) = (n^a)/(n^a) = 1
     
  4. Jun 16, 2006 #3
    Hehe math is so cool. Thanks.
     
  5. Jun 16, 2006 #4

    matt grime

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    Have a search for lots of posts on this topic on these forums; it is essentially a convention that allows us to coherently extend a definitions of powers.
     
  6. Jun 17, 2006 #5
    Alternatively, since na+b=nanb, then it must be that na=na+0=nan0, so n0 = 1.

    Except for n = 0, of course. There's a whole thread on that.
     
  7. Jun 17, 2006 #6

    matt grime

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    If we want to extend the definition from its natural domain consistently

     
  8. May 1, 2011 #7
    1 = (5^7)/(5^7)= 5^(7-7) = 1 Easy!!
     
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