Why is a number to the zero power always one?

Answer 1

So that it is consistent with power rules - 1 = x^a / x^a = x^(a-a) = x^0.

Answer 2

First, it isn't always one: 0 to the 0 power has no solution.

Think of it this way. Take any number and raise it to the fourth power, then third, then second, then first, then 0th power and you'll see why it works.

2^4 = 16
2^3 = 8 (16 divided by 2)
2^2 = 4 (8 divided by 2)
2^1 = 2 (4 divided by 2)
2^0 = 1 (2 divided by 2)

and this helps further with negative exponents

2^(-1) = 1/2 (1 divided by 2)
2^(-2) = 1/4 (1/2 divided by 2)

It doesn't matter what your base is, except zero, or course

5^4 = 625
5^3 = 125
5^2 = 25
5^1 = 5
5^0 = 1

~Bill

Answer 3

Your answer can be found right here:

http://mathforum.org/dr.math/faq/faq.number.to.0power.html

Guido