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

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```

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

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

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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