It is a Definition that N to the Zero Power is one.
In symbols: N^0=1

Many students feel confused by this definition and 
would like an explanation or justification why we 
use this rule.

This rule is consistent with many of our other rules 
of arithmetic and algebra. Notice that
3^4=81
3^3=27
3^2=9
3^1=3

The pattern you may notice above, is that if the power 
of three is reduced by one, this is like dividing by three. 
In other words:
(3^3)/3=27/3=9=3^2

So, dividing by three reduces the power by one.

Well, then, if we take three to the first power, which is 
three, and divide it by three we reduce it by a power to 
get three to the zero power. It seems reasonable that three 
divided by three should also equal one.
In symbols:

1 = (3/3)=(3^1)/3=3^0

A more algebraic argument could be made if you accept the 
following exponent rule:

(a^m)/(a^n)=a^(m-n)

Thus, if the exponents are both equal, you get:

a^0= a^(m-m)=(a^m)/(a^m)=1 since a non-zero number 
divided by itself is one.

 5 to the power of 2 is 25 (5^2=25), if you divide 25 by 25 you will get 1
Hence, 5^2 divide by 5^2 is one
Using the rule if the bases are the same, when dividing subtract the exponents.
therefore 5^2-2 = 5^0 = 1

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