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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] = ⏟.
Nicolas Chuquet (French:; born c. 1445 – c. 1455; died c. 1488 – c. 1500) was a French mathematician. He invented his own notation for algebraic concepts and exponentiation. He may have been the first mathematician to recognize zero and negative numbers as exponents. [1]
In the centuries following the initial statement of the result and before its general proof, various proofs were devised for particular values of the exponent n. Several of these proofs are described below, including Fermat's proof in the case n = 4, which is an early example of the method of infinite descent.
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The Born–Landé equation is a means of calculating the lattice energy of a crystalline ionic compound. In 1918 [ 1 ] Max Born and Alfred Landé proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]