why would anything to the zero power equal one according to division

Here's why 0^0 is undefined.....

Normally  a^n /a^n = a^(n-n) = a^0 =1

So....   0^a/0^a  should be  0^(a - a) = 0^0 =1....however, the problem is that we divided by 0 originally (0^a)....and that's undefined

$$\\\frac{5^7}{5^7}=5^{7-7}=5^0\\\\
$but$\\\\
$any non-zero number divided by itself $\\\\
so\\\\
5^0=1\\\\
$Anything (including 0) raised to the 0 power is 1 $$$

I would disagree that 0^0 = 1.

I believe that it is an indeterminate expression; which means that it can have any value, depending upon how it was created.

I do fully agree that a^0 = 1, whenever a ≠ 0.

Yes Geno you may be right.  I was thinking about this as well.  My initial thought was that it was undefined but then I hunted about on the net and found people disagreed with me.

There seemed to be a concesous of opinion that 0^0 was defined as 1  ( this is just one site that said this - there were others)

http://www.youtube.com/watch?v=CZWoAO6rwTM

However, looking at the site below I think I shall change my mind and say that 0^0 is undefined.

http://math.stackexchange.com/questions/11150/zero-to-the-zero-power-is-00-1

Thank you Gino.