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Fourth power. In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n4 as n “ tesseracted ”, “ hypercubed ...
The term power (Latin: potentia, potestas, dignitas) is a mistranslation [4] [5] of the ancient Greek δύναμις (dúnamis, here: "amplification" [4]) used by the Greek mathematician Euclid for the square of a line, [6] following Hippocrates of Chios. [7]
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
t. e. Power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. Power is a scalar quantity. Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle ...
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...
In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826. [1] Specifically, the power of a point with respect to a circle with center and radius is defined by. If is outside the circle, then , if is on the circle, then ...
Vieta's formulas relate the polynomial coefficients to signed sums of products of the roots r1, r2, ..., rn as follows: Vieta's formulas can equivalently be written as for k = 1, 2, ..., n (the indices ik are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the ...
Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive integer then 4 divides ( 2 n n ) {\displaystyle {\binom {2n}{n}}} if and only if n is not a power of 2.