Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:
just as multiplication by a positive integer corresponds to repeated addition:
The exponent is usually shown as a superscript to the right of the base. The exponentiation an can be read as: a raised to the n-th power, a raised to the power [of] n or possibly a raised to the exponent [of] n, or more briefly: a to the n-th power or a to the power [of] n, or even more briefly: a to the n. Some exponents have their own pronunciation: for example, a2 is usually read as a squared and a3 as a cubed.
The power an can be defined also when n is a negative integer, at least for nonzero a. No natural extension to all real a and n exists, but when the base a is a positive real number, an can be defined for all real and even complex exponents n via the exponential function ez. Trigonometric functions can be expressed in terms of complex exponentiation.
Exponentiation where the exponent is a matrix is used for solving systems of linear differential equations.
Exponentiation is used pervasively in many other fields as well, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public key cryptography.
Graphs of y=ax for various bases a: base 10 (green), base e (red), base 2 (blue), and base ½ (cyan). Each curve passes through the point (0,1) because any nonzero number raised to the power 0 is 1. At x=1, the y-value equals the base because any number raised to the power 1 is itself.
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HPCwire, CA - Nov 17, 2008
... application would require double-precision function units and instructions to facilitate such operations as random number generation and exponentiation , ...
knights
Sat, 14 Mar 2009 02:52:53 GM
Solve: 765 mod 13 by modular . exponentiation. Its easy to get the answer by using the mod, but im not 100% clear on how to solve this by modular . exponentiation. . Thanks!
