# Exponent

Exponent[expr,form]

gives the maximum power with which form appears in the expanded form of expr.

Exponent[expr,form,h]

applies h to the set of exponents with which form appears in expr.

# Details and Options • The default taken for h is Max.
• form can be a product of terms.
• Exponent works whether or not expr is explicitly given in expanded form.
• Exponent[0,x] is .
• Exponent[expr,{form1,form2,}] gives the list of exponents for each of the formi.

# Examples

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## Basic Examples(1)

Find the highest exponent of :

## Scope(4)

The degree of a polynomial:

Exponents may be rational numbers or symbolic expressions:

The lowest exponent in a polynomial:

The list of all exponents with which appears:

## Options(2)

### Modulus(1)

The degree of a polynomial over the integers modulo 2:

### Trig(1)

With Trig->True, Exponent recognizes dependencies between trigonometric functions:

## Properties & Relations(2)

The number of complex roots of a polynomial is equal to its degree:

Use Solve to find the roots:

Length of the CoefficientList of a polynomial is one more than its degree:

## Possible Issues(1)

Exponent is purely syntactical; it does not attempt to recognize zero coefficients:

Introduced in 1988
(1.0)
|
Updated in 1996
(3.0)
2003
(5.0)