Rational Exponents
A
rational
number is a real number that can be expressed as
a ratio of two finite integers:
Applying property (2) of exponents, we have
Thus, the only thing new is
. Since
we see that
is the
th root of
.
This is sometimes written
The
th root of a real (or complex) number is not unique. As we all
know, square roots give two values (
e.g.,
). In the
general case of
th roots, there are
distinct values, in
general. After proving
Euler's identity, it will be easy to find them
all (see §
3.11). As an example,
,
,
,
and
, since
.
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