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.

If you find errata in the math, bugs in the code of, or just want to say Eh, please send us a letter or join us on our roost: @rulesofalgebra.


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