Power
In its primary meaning (an integer and positive power), it is the product of a number of equal factors and is written in the form (
times), where
is the base,
the exponent and
the power. The basic properties of powers are:
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Further generalizations of the idea of a power include: zero powers: (when
); negative powers:
; fractional powers:
; and a power with an irrational exponent:
, where
is an arbitrary sequence of rational numbers tending to
. Powers with a complex base (see de Moivre formula) and powers with a complex base and complex exponent (by definition:
) are also studied.
Comments
Besides the three properties listed above there is a fourth:
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Together these four operations are called the laws of exponents.
Power. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Power&oldid=29404