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IEVref:102-02-07ID:
Language:enStatus: Standard
Term: exponentiation
Synonym1:
Synonym2:
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Definition: function assigning to any positive real number a and any real number b the positive real number denoted by a b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaiaadkgaaaaaaa@3AC7@ such that a 0 =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaKqzGdGaaGimaaaakiabg2da9KqzafGaaGymaaaa@3E62@ , a 1 =a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaKqzGdGaaGymaaaakiabg2da9iaadggaaaa@3DDF@ and a b+c = a b a c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaiaadkgacqGHRaWkcaWGJbaaaOGaeyypa0JaamyyamaaCaaaleqa baGaamOyaaaakiabgwSixlaadggadaahaaWcbeqaaiaadogaaaaaaa@43EA@ for any real numbers b and c

Note 1 to entry: The function which assigns to any real number x the number ax is the exponential function to the base a. The function which assigns to any positive real number x the number xb is a power function.

Note 2 to entry: The exponentiation can be extended to negative real number a and integer b, and to other mathematical entities, for example, complex numbers, matrices and scalar quantities.


Publication date:2008-08
Source:
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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