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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 15

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

$$\left({a \over b}\right)^{-n} = \left({b\over a}\right)^n$$
Description:

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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