Post a New Question

math (extra credit)!

posted by .

my teacher asked me why a number to the zero power is equal to 1. could you please explain why a number to the zero power equals 1?

  • math (extra credit)! -

    Consider first positive powers. Let's define:

    f(a,n) = a^n

    where a is a real number and n is a positive integer. This is well defined:

    f(a,n) = a^n =
    a*a*a...(n-factors in total).

    Now, we haven't defined f(a,n) when n is not a positive integer, so, in theory, you are free to extend the function f(a,n) in any arbitrary way to other numbers. However, the function
    f(a,n) has some nice properties and you want to preserve those when you extend the definition of f(a,n).


    f(a,n+m) = f(a,n)*f(a,m)

    If we want to extend the function to
    n = 0 while not violating this equation, then we must choose f(a,0)= 1. To see this, take m = 0, in the above equation:

    f(a,n) = f(a,n)*f(a,0) --->

    f(a,0) = 1.

    So, what mathematicians have done here (and in many other cases) is to take some of the properties of the function they want to extend to a larger set as the definition of the function (they uniquely define the function).

  • math (extra credit)! -

    thx but this didn't help i need to know why n^0= 1

  • math (extra credit)! -

    He told you, and I think it was the coolest answer yet!

Answer This Question

First Name
School Subject
Your Answer

Related Questions

More Related Questions

Post a New Question