What is "exponentiation"

exponentiation \exponentiation\ n. the process of raising a quantity to some assigned power.

Syn: involution.

n. 1 (context mathematics arithmetic uncountable English) The process of calculating a power by multiplying together a number of equal factors, where the exponent specifies the number of factors to multiply. 2 (context mathematics arithmetic countable English) A mathematical problem involving exponentiation.

n. the process of raising a quantity to some assigned power [syn: involution]

Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b is the product of multiplying n bases:

$$b^n = \underbrace{b \times \cdots \times b}_n$$

In that case, b is called the n-th power of b, or b raised to the power n.

The exponent is usually shown as a superscript to the right of the base. Some common exponents have their own names: the exponent 2 (or 2nd power) is called the square of b (b) or b squared; the exponent 3 (or 3rd power) is called the cube of b (b) or b cubed. The exponent −1 of b, or , is called the reciprocal of b.

When n is a negative integer and b is not zero, b is naturally defined as 1/b, preserving the property .

The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.

Exponentiation is used extensively in many fields, 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.