(linguistics)
An exponent is a phonological manifestation of a morphosyntactic property. In non-technical language, it is the expression of one or more grammatical properties by sound. There are several kinds of exponents:

• identity
• affixation
• reduplication
• internal modification

(please note these examples will use regular orthography rather than phonetic transcription due to the lack of IPA support in HTML)

Identity

An identity exponent is both simple and common: it has no phonological manifestation at all.

English Example:
DEER + PLURAL ---> deer

Affixation

Affixation is the addition of a prefix, suffix, or infix to a word.

English Example:
WANT + PAST ---> wanted

Reduplication

Reduplication is the repetition of part of a word.

Sanskrit Example:
DA ('give') + PRESENT + ACTIVE + INDICATIVE + FIRST PERSON + SINGULAR --> dadaami (the da at the beginning is from reduplication, a characteristic of class 3 verbs in Sanskrit)

Internal Modification

There are several types of internal modification. An internal modification may be segmental, meaning it changes a sound in the root.

English Example:
STINK + PAST = stank (i becomes a)

An internal modification might be a suprasegmental modification. An example would be a change in pitch.

A slightly controversial exponent is subtraction, in which a sound or group of sounds is removed. Some people don't think this happens.

(Sources: Typology lectures by Dr. Greg Stump, University of Kentucky)

Exponents

Just like multiplication is a repitition of addition, exponents are a repitition of multiplication. An exponent looks like this: b^x. b would be the base , and x would be the exponent. In 5², 5 is the base and 2 is the exponent.

What this all means is: you take the base, and you multiply it against it self as many times as the exponent. 2⁴ would be 2 ⋅ 2 ⋅ 2 ⋅ 2 = 16. 5³ = 5 ⋅ 5 ⋅ 5 = 125. If the exponent is 2, then you say "squared". If it is 3, you say "cubed". If its bigger than that then you just say "to the x^th power". This all assumes that the exponent isn't 0. If it is, in fact, 0, the whole thing comes out to 1. That's right. 5⁰ = 1. 19⁰ = 1. (22² + (9*5))⁰ = 1. That's just the way things are.

There are a few basic laws of exponents:

Multiplying exponents: b^a + b^q. This means p² + p⁵ = p⁷. 5² + 5⁴ = 5⁶ = 15625

Power of a power: (b^s)^t = b^st. (5²)³ = 5⁶ = 15625

Power of a product: (ab)^c = a^cb^c.

Power of a fraction: (a/b)^q = a^q/b^q

Division of powers: b^q/b^m = b^q-m. 5³/5¹ = 5^3-1 = 5² = 25.

Simple, huh?

Ex*po"nent (?), n. [L. exponens, -entis, p. pr. of exponere to put out, set forth, expose. See Expound.]

1. Alg.

A number, letter, or any quantity written on the right hand of and above another quantity, and denoting how many times the latter is repeated as a factor to produce the power indicated

; thus a² denotes the second power, and aⁿ the xth power, of a (2 and x being the exponents). A fractional exponent, or index, is used to denote the root of a quantity. Thus, a^ࡩ denotes the third or cube root of a.

2.

One who, or that which, stands as an index or representative; as, the leader of a party is the exponent of its principles.

Exponent of a ratio, the quotient arising when the antecedent is divided by the consequent; thus, 6 is the exponent of the ratio of 30 to 5. [R.]

 

© Webster 1913.