SOLUTION: I am interested in finding a simple explanation as to why a number taken to a zero power is equal to 1. Thanks.

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Question 150035: I am interested in finding a simple explanation as to why a number taken to a zero power is equal to 1.
Thanks.
Found 3 solutions by edjones, Fombitz, scott8148:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
For any number:
n^x/n^y=n^(x-y)
.
If x=y then x/y=1
and n^x/n^y=n^0=1
.
Ed

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The simplest explanation is because someone said so.
From exponentiation, you know the division rule that,
x%5EM%2Fx%5EN=X%5E%28M-N%29
If M=N, then
x%5EM%2Fx%5EM=x%5E%28M-M%29
1=x%5E%280%29
If it was not the case, then that example wouldn't hold up.
You would disprove the division rule.
Your mathematical system would fall apart.
That definition is that way so that your mathematical system remains sound and consistent.
That's a simple answer, but it's actually a very complicated question.


Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
demonstration is the most straight forward

using rules for exponents, (x^a)/(x^b)=x^(a-b) __ (x^5)/(x^3)=x^2 __ (x*x*x*x*x)/(x*x*x)=x*x

suppose a=b __ (x^a)/(x^b)=x^(a-b)=x^0 __ (x*x*x)/(x*x*x)=1=x^0