If n is a positive integer and x is any real number, then
xn corresponds to repeated multiplication:
xn = x × x × ⋯ × x (n times).
We can call this “x raised to the power of n,”
“x to the power of n,” or simply “x to the n.”
Here, x is the base and n is the exponent (or power).
From this definition, we can deduce some basic rules that exponentiation must follow,
as well as some special cases that arise from these rules. In the process, we will
define exponentials xa for exponents a that are not positive integers.
The rules and special cases are summarized in the following table. Below,
we provide details for each one. |
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