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 Depdendent Variable

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 Dependent Variable

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# 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)

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:

We will need to be able to cancel complicated exponential expressions quickly and accurately (especially for infinite series).

We also need to be able to reorganize exponential functions so that the role of the variable is clear.