Laws of Exponents
There are only four major laws of exponents that determine all
that we do with exponents and exponential functions. Assume a and
b are positive real numbers, while x and y are any real numbers
(possibly negative or irrational)
![](./articles_imgs/425/pic1.gif)
Notice the second law implies , so we
can think of a negative in an exponent as sending that
piece to the denominator. These rules can also be combined
to form more complicated statements. Here are some examples:
![](./articles_imgs/425/pic3.gif)
We will need to be able to cancel complicated exponential
expressions quickly and accurately (especially for infinite
series).
![](./articles_imgs/425/pic4.gif)
We also need to be able to reorganize exponential functions so
that the role of the variable is clear.
![](./articles_imgs/425/pic5.gif)
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