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A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent . Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times. [ 1][ 2] The first ten powers of 2 for non-negative values of n are:
Mean square. In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. [ 1] It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the ...
Square (algebra) 5⋅5, or 52 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.
e. In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as " b (raised) to the (power of) n ". [ 1]
In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. [ 1] Given a set , its RMS is denoted as either or . The RMS is also known as the quadratic mean (denoted ), [ 2][ 3] a special case of the generalized mean. The RMS of a continuous function is denoted and can be ...
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 ...
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as a sum of four non-negative integer squares. [1] That is, the squares form an additive basis of order four. where the four numbers are integers. For illustration, 3, 31, and 310 in several ways, can be represented as the sum ...
Generalized mean. Plot of several generalized means . In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) [ 1] are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means ( arithmetic, geometric, and harmonic means ).