Exponentiation

"Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, Mathematica, and many other computer languages, exponentiation is denoted with a caret, i.e., as b^e. However, in FORTRAN, it is denoted b**e"

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"If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication
xn=x×x×⋯×x
        ____________
               n times
    
 x×x×⋯×x

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."

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@Math Insight