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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Modulus  
Trig  
Applications  
Properties & Relations  
Possible Issues  
See Also
Tech Notes
Related Guides
History
Cite this Page

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 -Infinity.
  • Exponent[expr,{form1,form2,…}] gives the list of exponents for each of the formi.
  • Exponent takes the following options:
  • Modulus 0modulus to assume for integers
    Trig Falsewhether to do trigonometric as well as algebraic transformations

Examples

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Basic Examples  (1)

Find the highest exponent of :

Wolfram Language code: Exponent[1 + x ^ 2 + a x ^ 3, x]

Scope  (4)

The degree of a polynomial:

Wolfram Language code: Exponent[(x ^ 2 + 1) ^ 3 + 1, x]

Exponents may be rational numbers or symbolic expressions:

Wolfram Language code: Exponent[x ^ (n + 1) + 2 Sqrt[x] + 1, x]

The lowest exponent in a polynomial:

Wolfram Language code: Exponent[(x ^ 2 + 1) ^ 3 - 1, x, Min]

The list of all exponents with which appears:

Wolfram Language code: Exponent[1 + x ^ 2 + a x ^ 3, x, List]

Options  (2)

Modulus  (1)

The degree of a polynomial over the integers modulo 2:

Wolfram Language code: Exponent[2x ^ 2 - x + 1, x, Modulus -> 2]

Trig  (1)

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

Wolfram Language code: Exponent[Tan[x], Cos[x], Trig -> True]

Applications  (1)

Compute the leading coefficient:

Wolfram Language code: LeadingCoefficient[poly_, x_] := Coefficient[poly, x, Exponent[poly, x]]
Wolfram Language code: LeadingCoefficient[2 + 3x + 17x ^ 5, x]

Compute the leading term:

Wolfram Language code: LeadingTerm[poly_, x_] := With[{n = Exponent[poly, x]}, Coefficient[poly, x, n]x ^ n]
Wolfram Language code: LeadingTerm[2 + 3x + 17x ^ 5, x]

Properties & Relations  (2)

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

Wolfram Language code: f = (x + 1) ^ 5 - 2x + 3;
Wolfram Language code: Exponent[f, x]

Use Solve to find the roots:

Wolfram Language code: Length[x /. Solve[f == 0, x]]

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

Wolfram Language code: f = (x ^ 2 + 2x - 1) ^ 7 - 3;
Wolfram Language code: Exponent[f, x]
Wolfram Language code: Length[CoefficientList[f, x]]

Possible Issues  (1)

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

Wolfram Language code: zero = Sqrt[2] + Sqrt[3] - Sqrt[5 + 2Sqrt[6]]; f = zero x ^ 2 + x + 1;
Wolfram Language code: Exponent[f, x]
Wolfram Language code: Exponent[RootReduce[f], x]
Wolfram Research (1988), Exponent, Wolfram Language function, https://reference.wolfram.com/language/ref/Exponent.html (updated 2003).

Text

Wolfram Research (1988), Exponent, Wolfram Language function, https://reference.wolfram.com/language/ref/Exponent.html (updated 2003).

CMS

Wolfram Language. 1988. "Exponent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/Exponent.html.

APA

Wolfram Language. (1988). Exponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Exponent.html

BibTeX

@misc{reference.wolfram_2026_exponent, author="Wolfram Research", title="{Exponent}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Exponent.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_exponent, organization={Wolfram Research}, title={Exponent}, year={2003}, url={https://reference.wolfram.com/language/ref/Exponent.html}, note=[Accessed: 13-June-2026]}