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 .