SOLUTION: Earlier I asked why any number that has "zero" as the exponent equals 1. It was answered by saying that the answer will always be 1. But my question is WHY is the answer always o

Algebra ->  Exponents -> SOLUTION: Earlier I asked why any number that has "zero" as the exponent equals 1. It was answered by saying that the answer will always be 1. But my question is WHY is the answer always o      Log On


   



Question 28164: Earlier I asked why any number that has "zero" as the exponent equals 1. It was answered by saying that the answer will always be 1. But my question is WHY is the answer always one. An exponent tells you how many times to multiply a number. If that number is multiplied to the 2nd power, then you would multiply it twice. If it is to the zero power, then it should be multiplied zero times, but the answer is "1". WHY is this?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
One rule of Powers is:

+a%5Em%2Fa%5En+=+a%5E%28m-n%29+

Now, what if the 2 powers, m and n were the same number? Here:

+a%5Em%2Fa%5Em+=+a%5E%28m-m%29+

The lefthand side is 1, the righthand side becomes a%5E0. This is where a%5E0=1 comes from.

jon.