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In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
The sum of the reciprocals of the squared powers of two (powers of four) is 1/3. The smallest natural power of two whose decimal representation begins with 7 is [11] = Every power of 2 (excluding 1) can be written as the sum of four square numbers in 24 ways. The powers of 2 are the natural numbers greater than 1 that can be written as the sum ...
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.. For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10:
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [1] In his 1947 paper, [2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations.
Examples of equally spaced values are 10, 100, 1000, 10000, and 100000 (i.e., 10 1, 10 2, 10 3, 10 4, 10 5) and 2, 4, 8, 16, and 32 (i.e., 2 1, 2 2, 2 3, 2 4, 2 5). Exponential growth curves are often depicted on a logarithmic scale graph. A logarithmic scale from 0.1 to 100 The two logarithmic scales of a slide rule
5⋅5, or 5 2 (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.
It is a binary operation defined with two numbers a and b, where a is tetrated to itself b − 1 times. The type of hyperoperation is typically denoted by a number in brackets, []. For instance, using hyperoperation notation for pentation and tetration, 2 [ 5 ] 3 {\displaystyle 2[5]3} means tetrating 2 to itself 2 times, or 2 [ 4 ] ( 2 [ 4 ] 2 ...
In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. [1] Other symbols include punctuation marks and brackets, used for grouping where there is not a well-defined order of operations.