| Basic rules for exponentiation
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 the power.
From this definition, we can deduce some basic rules that exponentiation must follow as well as some hand special cases that follow from the rules. In the process, we'll define exponentials xa
for exponents a
that aren't positive integers.
The rules and special cases are summarized in the following table. Below, we give details for each one.
From this definition, we can deduce some basic rules that exponentiation must follow as well as some hand special cases that follow from the rules.
The rules and special cases are summarized in the following table. Below, we give details for each one. |
English
