IEC 60050 - International Electrotechnical Vocabulary

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IEVref:	102-02-07		ID:
Language:	en		Status: Standard

Term:	exponentiation
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Definition:	function assigning to any positive real number a and any real number b the positive real number denoted by $a^{b}$ such that $a^{0} = 1$ , $a^{1} = a$ and $a^{b + c} = a^{b} \cdot a^{c}$ for any real numbers b and c Note 1 to entry: The function which assigns to any real number x the number a^x is the exponential function to the base a. The function which assigns to any positive real number x the number x^b 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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ab a b MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaiaadkgaaaaaaa@3AC7@ 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@ a b+c = a b ⋅ a c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaahaaWcbe qaaiaadkgacqGHRaWkcaWGJbaaaOGaeyypa0JaamyyamaaCaaaleqa baGaamOyaaaakiabgwSixlaadggadaahaaWcbeqaaiaadogaaaaaaa@43EA@ bcNote 1 to entry: The function which assigns to any real number x the number a^x is the exponential function to the base a. The function which assigns to any positive real number x the number x^b 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.