# Algebrarules.com

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

$$123^0 = 1 = \pi^0 = 1 = (everything)^0 = 1$$
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## A little bit about algebrarules.com

Algebra rules is a project by two of the folks who run The Autodidacts.

A couple of autodidact math enthusiasts, we were looking for all the rules of basic algebra concisely presented in one place. We couldn’t find such a place, so we made Algebrarules.com

These simple rules — applied with a pinch of imagination and a dash of arithmetic — can divide, conquer, and solve just about any practical algebra problem.

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