Algebrarules.com

The most useful rules of basic algebra,
free, simple, & intuitively organized
X

Howdy! Here are a few very handy rules of algebra. These basic rules are useful for everything from figuring out your gas mileage to acing your next math test — or even solving equations from the far reaches of theoretical physics. Happy calculating!

Algebra Rule 18

Anything raised to the power of zero is equal to 1

$$a^0 = 1$$
Description:

This rule may seem arbitrary, but it is necessary in order to maintain consistency with other properties of exponents. Consider the rule $a^na^m = a^{n+m}$. What happens if $m = 0$? The right hand side of the equation will be $a^{n+0}$, or $a^n$. This means that in the left hand side, $a^n$ has to be multiplied by the value of $a^0$, but remain unchanged. The only way for this to be the case is if $a^0 = 1$. (For some discussion of the peculiar case of $0^0$ and why it should (probably) equal $1$, see this article.)

$$123^0 = 1 = \pi^0 = 1 = (everything)^0 = 1$$
« Previous Rule Next Rule »