Algebrarules.com

The most useful rules of basic algebra,
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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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