Exponentiation

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:

The exponent is usually shown as a superscript to the right of the base. The exponentiation xn can be read as: x raised to the n-th power or x raised to the power n, or more briefly: x to the n-th power or x to the power n. Some exponents can be read in a certain way; for example x2 is usually read as x squared and x3 as x cubed.

Exponentiation can also be defined when the exponents are negative integers, and more generally, for any real number(or even complex numbers). Further generalizations of the exponentiation operation, including complex numbers and matrices, can be found in many branches of mathematics. Another historical synonym, involution, is now rare and should not be confused with its more common meaning.

Exponentiation is a basic mathematical tool that 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.