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 15

A fraction raised to a negative exponent equals the inverse of the fraction raised to a positive exponent

```\left({a \over b}\right)^{-n} = \left({b\over a}\right)^n```

The reciprocal of a fraction is the fraction turned on its head: the reciprocal of ``{2 \over 3}`` is ``{3 \over 2}``. We know from the previous rule that ``a^{-n}`` is the reciprocal of ``a^n``, so we can simply convert the fraction to its reciprocal by exchanging the numerator and denominator, and then the exponent becomes positive. Positivity is such a nice thing!

```\left({1 \over 2} \right)^{-2} = {1 \over (1/2)*(1/2)} = {1 \over 1/4} = 4 = 2^2 = \left({2\over1} \right)^2```
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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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