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(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: (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)