Why does everything to the zero power equal one?

Answer 1

The easiest way to see this is to consider what happens when you have a base raised to an exponent and divide it by that base. Consider:

x10 / x = x9

x9 / x = x8

Or more generically:

xn / x = xn - 1

Logically then, we can extend this all the way down to one:

x1 / x = x0

And what is x1 / x? That's simply x/x of course, so we have:

x0 = x/x

x0 = 1

So with the exception of zero, anything to the power of zero is equal to one. A base of zero is an exception here. Using the same logic consider what it would mean:

00 = 01/0

That would give us zero divided by zero, which is undefined, hence the 00 being undefined as well.