## AMA Manual of Style - Stacy L. Christiansen, Cheryl Iverson 2020

# Exponents

Mathematical Composition

**20.3.1 Fractional Exponents vs Radicals.**

Use of radicals (eg, any expression that contains a radical symbol: √) may sometimes be avoided by substituting a fractional exponent:

As with unstacking fractions, if clarity is sacrificed by making the equation fit within the text, it is preferable to set it off. For example, *E* = 1.96{[*P*(1 − *P*)]/*m*}^{1/2} may fit within the text, but the equation set off and centered as below might be more easily understood:

**20.3.2 Negative Exponents.**

A negative exponent denotes the reciprocal of the expression, as illustrated in these examples:

**20.3.3 Logarithmic Expressions.**

The term *log* is an abbreviation of *logarithm*. A system of logarithms may be based on any number, although logarithmic systems based on the numbers 10, 2, and the irrational number *e* are most common. The base should be subscripted and follow the word *log*. In the following examples, note that logarithms are always computed from exponents of the number that forms their basis.

Logarithms based on *e* are called *natural logarithms* and are often represented as *ln*.

The terms “*e ^{x}*” and “exp

*x*” are identical in meaning and are interchangeable. The latter is preferable for constructions that involve additional subscripts or superscripts. For instance, exp (

*x*

^{3}− 1) is identical to

*e*

^{x}^{3−1}, but the former is preferred because it is easier to read and typeset.