Power
From Encyclopedia of Mathematics
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:
 |
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:
 |
Together these four operations are called the laws of exponents.
How to Cite This Entry:
Power. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Power&oldid=15779
Power. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Power&oldid=15779
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article