# 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 17

#### If the top and bottom of a fraction are both exponents with the same base, the fraction is equal to the base raised to the numerator exponent minus the denominator exponent

$${a^n\over a^m} = a^{n-m}$$
Description:

This one is very simple. Since division is the inverse of multiplication, multiplying a number by itself a few times and then dividing it by itself multiplied a few time is the same as just multiplying it by itself a few less times.

$${4^4\over4^2} = {4*4*4*4 \over 4*4} = {256 \over 16} = { 16 \over 1} = 16 = 4^2 = 4^{4-2}$$
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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.

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

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