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Exponentiation

*"*Here is as good a place as any to introduce into our logical discussion of the real number system the notion of exponentiation with integral exponents. If *a* [is a real number] and *n* is some positive integer, we define to be *a*·*a*·*a*···*a* (*n* times), and if *a* [is not equal to zero], , . From these definitions we immediately derive the usual rules of exponentiation, in particular , , [and] .*"* *(see ita-2-2-16-pg21)*

The 'usual rules of exponentiation' are evident from the definition of exponentiation where the exponent, *n*, is positive. The rationale when the exponent is zero or negative requires calculus. However, given that we have chosen as the symbol for the multiplicative inverse, we can note the following:

Below are some examples of exponentiation in *Mathematica*.

Converted [ in part ] by *Mathematica*
December 4, 2007