0 Power

Date: 8/4/96 at 16:1:48
From: Jeffrey Paul Goins
Subject: Power 0

Dear Dr. Math,

Why is any number to the 0 power equal to one?

Thank you!

Levi Goins

Date: 8/5/96 at 11:29:51
From: Doctor Anthony
Subject: Re: Power 0

The rules of algebra are designed to be consistent as far as this is 
possible.

Why is anything to power 0 equal to 1?

Consider first  a^5/a^3    As you know this is the same as 

    (a*a*a*a*a)/(a*a*a) = a^2

So to get the result we subtracted the powers to give 5-3 = 2

What about (a*a*a)/(a*a*a) = a^(3-3) = a^0

But we know that a^3/a^3 = 1, and so a^0 = 1

This does not depend on a, and is true in the general case.   

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/