• identity
• affixation
• reduplication
• internal modification

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

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.