related topics
{math, number, function}
{math, energy, light}
{language, word, form}
{rate, high, increase}
{acid, form, water}
{mi², represent, 1st}
{style, bgcolor, rowspan}

Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a:

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 as 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, 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.


Full article ▸

related documents
Model theory
Vector space
Fourier transform
Propositional calculus
Lisp (programming language)
Vienna Development Method
Group (mathematics)
C (programming language)
Generic programming
Clifford algebra
Floating point
Discrete Fourier transform
First-order logic
Euclidean vector
Ordinal number
Mathematical logic
Regular expression
Emmy Noether
Surreal number
Prime number
Singular value decomposition
Radix sort
Natural deduction
Gödel's incompleteness theorems
System of linear equations
Combinatory logic