# Proof That Any Number Raised to 0 Equals 1

You have learned before that any number raised to 0 equals 1. But did you ever wonder why any non-zero number when raised to 0 equals 1? Here’s a very simple explanation.

We know that when we divide an expression with exponents having the same base, we subtract the exponents. That is, for any non-zero $x$,

$\displaystyle \frac{x^m}{x^n} = x^{m-n}$.

Now, in the equation above, the only possible for the exponent to be 0, is if the minuend and subtrahend are equal. That is,

$x^0 = x^{m-m}$

However,

$x^{m-m} = \displaystyle \frac{x^m}{x^m} = 1$.

Therefore, $x^0 = 1$