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Power Of 0 = 1 (Explain Please)

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data
    For part of my homework i need to explain:
    Why does any number with a power of zero have a value of 1?


    2. Relevant equations
    100^0=1
    81^0=1
    5^0=1


    3. The attempt at a solution
     
  2. jcsd
  3. Nov 6, 2008 #2

    mgb_phys

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    Look at the exponential sequence if you write down the positive and negative powers of a number
    eg 3:
    3^-3 = 1/27
    3^-2 = 1/9
    3^-1 = 1/3
    3^0 = 1
    3^1 = 3
    3^2 = 9
    3^3 = 27

    What's the pattern between each value?

    edit fixed formating
     
    Last edited: Nov 6, 2008
  4. Nov 6, 2008 #3
    I really don't know. Could you please give me the answer.
     
  5. Nov 6, 2008 #4

    Borek

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    Check what happens if you multiply 3*1/27, 3*1/9...
     
  6. Nov 6, 2008 #5
    Yeah but how do i explain why does any number with a power of 0 have a value of 1
     
  7. Nov 6, 2008 #6

    Gokul43201

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    1. Do you know how to expand [itex]n^{b+c}[/itex]?

    2. Now, if you set [itex]b+c=0[/itex], write b in terms of c, and repeat step 1, what do you get?
     
  8. Nov 6, 2008 #7

    mgb_phys

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    Because if you divide "any number" by itself you get 1 and if you multiply "1/any number" by "any number". Just look at the above example with any other number than 3.
     
  9. Nov 6, 2008 #8
    You know the rules for adding/subtracting exponents?

    (a^b)*(a^c) = a^(b+c)

    and

    (a^b)/(a^c) = a^(b-c).

    What happens when b = c?

    You get (a^b)/(a^b) = a^(b-b) = a^0. But if you look to the LHS, you will see we have a number divided by itself which is 1.

    Incidentally, it is not true that 'any number' to the power of 0 = 1: 0^0 is undefined.
     
  10. Nov 7, 2008 #9
    As others explained, ab*ac=ab+c. Now try for example:
    3-1*31=3/3=1
    Same if you write as:
    3-1+1=30=1.

    Do you know how to explain now?
     
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