# 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:

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.

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Power.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Power&oldid=15779