Why is that any number raised to the power zero is one?

Answer 1

A simple proof is as follows: When dividing two numbers that are the same, but raised to different powers, you simply subtract the powers to get the answer. For example:

5^4 / 5^2 = 5^(4-2) = 5^2 = 25.

You can do this manually with 5^4 = 625 and 5^2 = 25. 625/25 = 25.

Now use the same power.

5^3 / 5^3 = 5^(3-3) = 5^0 = ?

Our question mark is easily answered. Any number divided by itself is 1. So 5^0 = 1. More generally, x^y / x^y = x^(y-y) = x^0 = 1.