What does exponent mean?

Definitions for exponent
ɪkˈspoʊ nənt or, esp. for 3 , ˈɛk spoʊ nəntex·po·nent

This dictionary definitions page includes all the possible meanings, example usage and translations of the word exponent.

Princeton's WordNet

  1. advocate, advocator, proponent, exponentnoun

    a person who pleads for a cause or propounds an idea

  2. exponentnoun

    someone who expounds and interprets or explains

  3. exponent, power, indexnoun

    a mathematical notation indicating the number of times a quantity is multiplied by itself

GCIDE

  1. Exponentnoun

    one who explains, expounds, or interprets.

Wiktionary

  1. exponentnoun

    One who expounds, represents or advocates

  2. exponentnoun

    The power to which a number, symbol or expression is to be raised. For example, the 3 in x.

Samuel Johnson's Dictionary

  1. EXPONENTnoun

    Exponent of the ratio, or proportion between any two numbers or quantities, is the exponent arising when the antecedent is divided by the consequent: thus six is the exponent of the ratio which thirty hath to five. Also a rank of numbers in arithmetical progression, beginning from 0, and placed over a rank of numbers in geometrical progression, are called indices or exponents: and in this is founded the reason and demonstration of logarithms; for addition and subtraction of these exponents answers to multiplication and division in the geometrical numbers. John Harris

    Etymology: from expono, Latin.

Wikipedia

  1. exponent

    Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the (power of) n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base. In that case, bn is called "b raised to the nth power", "b (raised) to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth". Starting from the basic fact stated above that, for any positive integer n {\displaystyle n} , b n {\displaystyle b^{n}} is n {\displaystyle n} occurrences of b {\displaystyle b} all multiplied by each other, several other properties of exponentiation directly follow. In particular: In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. From this basic rule that exponents add, we can derive that b 0 {\displaystyle b^{0}} must be equal to 1, as follows. For any n {\displaystyle n} , b 0 ⋅ b n = b 0 + n = b n {\displaystyle b^{0}\cdot b^{n}=b^{0+n}=b^{n}} . Dividing both sides by b n {\displaystyle b^{n}} gives b 0 = b n / b n = 1 {\displaystyle b^{0}=b^{n}/b^{n}=1} . The fact that b 1 = b {\displaystyle b^{1}=b} can similarly be derived from the same rule. For example, ( b 1 ) 3 = b 1 ⋅ b 1 ⋅ b 1 = b 1 + 1 + 1 = b 3 {\displaystyle (b^{1})^{3}=b^{1}\cdot b^{1}\cdot b^{1}=b^{1+1+1}=b^{3}} . Taking the cube root of both sides gives b 1 = b {\displaystyle b^{1}=b} . The rule that multiplying makes exponents add can also be used to derive the properties of negative integer exponents. Consider the question of what b − 1 {\displaystyle b^{-1}} should mean. In order to respect the "exponents add" rule, it must be the case that b − 1 ⋅ b 1 = b − 1 + 1 = b 0 = 1 {\displaystyle b^{-1}\cdot b^{1}=b^{-1+1}=b^{0}=1} . Dividing both sides by b 1 {\displaystyle b^{1}} gives b − 1 = 1 / b 1 {\displaystyle b^{-1}=1/b^{1}} , which can be more simply written as b − 1 = 1 / b {\displaystyle b^{-1}=1/b} , using the result from above that b 1 = b {\displaystyle b^{1}=b} . By a similar argument, b − n = 1 / b n {\displaystyle b^{-n}=1/b^{n}} . The properties of fractional exponents also follow from the same rule. For example, suppose we consider b {\displaystyle {\sqrt {b}}} and ask if there is some suitable exponent, which we may call r {\displaystyle r} , such that b r = b {\displaystyle b^{r}={\sqrt {b}}} . From the definition of the square root, we have that b ⋅ b = b {\displaystyle {\sqrt {b}}\cdot {\sqrt {b}}=b} . Therefore, the exponent r {\displaystyle r} must be such that b r ⋅ b r = b {\displaystyle b^{r}\cdot b^{r}=b} . Using the fact that multiplying makes exponents add gives b r + r = b {\displaystyle b^{r+r}=b} . The b {\displaystyle b} on the right-hand side can also be written as b 1 {\displaystyle b^{1}} , giving b r + r = b 1 {\displaystyle b^{r+r}=b^{1}} . Equating the exponents on both sides, we have r + r = 1 {\displaystyle r+r=1} . Therefore, r = 1 2 {\displaystyle r={\frac {1}{2}}} , so b = b 1 / 2 {\displaystyle {\sqrt {b}}=b^{1/2}} . The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.

ChatGPT

  1. exponent

    An exponent refers to the number of times a number or a mathematical expression, known as the base, is multiplied by itself. It is written as a superscript next to the base. For example, in the expression 2^3, 2 is the base and 3 is the exponent, meaning that 2 is multiplied by itself 3 times (2*2*2).

Webster Dictionary

  1. Exponentnoun

    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. Exponentnoun

    one who, or that which, stands as an index or representative; as, the leader of a party is the exponent of its principles

  3. Etymology: [L. exponens, -entis, p. pr. of exponere to put out, set forth, expose. See Expound.]

Wikidata

  1. Exponent

    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: ⁕Identity ⁕Affixation ⁕Reduplication ⁕Internal modification ⁕Subtraction

Chambers 20th Century Dictionary

  1. Exponent

    eks-pō′nent, n. he who, or that which, points out, or represents: (alg.) a figure which shows how often a quantity is to be multiplied by itself, as a3: an index: an example, illustration.—adj. Exponen′tial (alg.), pertaining to or involving exponents.—n. an exponential function.—Exponential curve, a curve expressed by an exponential equation; Exponential equation, one in which the x or y occurs in the exponent of one or more terms, as 5x = 800; Exponential function, a quantity with a variable exponent; Exponential series, a series in which exponential quantities are developed; Exponential theorem gives a value of any number in terms of its natural logarithm, and from it can at once be derived a series determining the logarithm. [L. exponensex, out, ponĕre, to place.]

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Numerology

  1. Chaldean Numerology

    The numerical value of exponent in Chaldean Numerology is: 8

  2. Pythagorean Numerology

    The numerical value of exponent in Pythagorean Numerology is: 5

Popularity rank by frequency of use

exponent#10000#23874#100000

Translations for exponent

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"exponent." Definitions.net. STANDS4 LLC, 2024. Web. 24 Apr. 2024. <https://www.definitions.net/definition/exponent>.

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