Some Exponent Help

[jrahhali]

i use the laws of exponents a lot, but today, i found myself asking the question "why?", STUPID JAVA and yahoo chat were being very fickle loading. So it brought me here, to the, really, smart people.

using the number 5 as an example:
5^2 = 5x5 (or is it?)
5^1 = 5x1 (?)
so what is
5^0 = ?? = 1 (?)

so my question is, why is x^n = 1 (where x not equal to zero) ?

[jrahhali]

Ah nvm. Thank's to my sister in law, she did some google search that i thought would turn up ugly results, but she found the answer: http://www.mathforum.org/dr.math/faq...to.0power.html
i can finally move on with my life!
basically it sais this:

soem reasoning:

3^1 = 3,
3^2 = 9
3^3 = 27
3^4 = 81

so, we can condlude that going down the list, you multiply by 3 and going up the list, you diving by 3.
therefore,

3^0 = 3/3 = 1!!!


R.T.P. x^0 = 1
recall, from the laws of exponents, x^a/x^b = x^(a-b)
therfore, x^a/x^a = x^(a-a) = x^0 = 1!!!!!!!
therefore, x^0 = 1!!!!!!!!!!!!
(the !'s were my addition =D)

so this thread can be deleted or closed, or whatever. or left for reference. boy, am i ever excited! BOY!! =p

EDIT: her google serch was "why exponent zero is one" hehe