Why is any nonzero number to the power of zero equal to one?

The rule comes from keeping exponent laws consistent. For a nonzero number $a$, we want $$\frac{a^m}{a^n}=a^{m-n}.$$ Now set $m=n$. Then $$\frac{a^n}{a^n}=1,$$ but the exponent rule says this should also be $$a^{n-n}=a^0.$$ So for every nonzero $a$, $$a^0=1.$$ You can also see the pattern by dividing by $a$ each step: $$a^3,\ a^2,\ a^1,\ a^0.$$ Going backward divides by $a$, so $a^0$ must be $1$. The phrase "any number" needs care: $0^0$ is a special indeterminate case in many contexts.