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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] = ⏟.
In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally similar to the trigonometric functions. Inverse hyperbolic functions: inverses of the hyperbolic functions, analogous to the inverse circular functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials.
The repetition threshold of an alphabet A of n letters is the minimum critical exponent of infinite words over A: clearly this value RT(n) depends only on n.For n=2, any binary word of length four has a factor of exponent 2, and since the critical exponent of the Thue–Morse sequence is 2, the repetition threshold for binary alphabets is RT(2) = 2.
For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is not algebraic.
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
The term 'expression' is part of the language of mathematics, that is to say, it is not defined within mathematics, but taken as a primitive part of the language. To attempt to define the term would not be doing mathematics, but rather, one would be engaging in a kind of metamathematics (the metalanguage of mathematics), usually mathematical logic.
Jeake's text appears to designate a written exponent of 0 as being equal to an "absolute number, as if it had no Mark", thus using the notation x 0 to refer to an independent term of a polynomial, while a written exponent of 1, in his text, denotes "the Root of any number" (using root with the meaning of the base number, i.e. its first power x ...