exponent

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exponent in mathematics, a number, letter, or algebraic expression written above and to the right of another number, letter, or expression called the base. In the expressions x² and xⁿ , the number 2 and the letter n are the exponents respectively of the base x. The exponent indicates the power to which the base is to be raised. When exponents were first introduced, only positive whole numbers were used, and the exponent indicated how many times the base was to be taken as a factor; e.g., 2 ⁵ =32, or 2·2·2·2·2=32. In advanced algebra, fractions, zero, and negative numbers are also used as exponents. Particular meanings have been assigned to these types of exponents so that they obey the same algebraic rules as does the simpler type of exponent. A fractional exponent such as 1/4 or 1/ n indicates the fourth or n th root , respectively, of the base. Any nonzero quantity raised to the zero power equals one; e.g., x⁰ =5 ⁰ =( a² + b² ) ⁰ =1. A negative exponent indicates the reciprocal of the quantity; e.g., x^-2 means 1/ x² . When quantities of the same base are multiplied together, their exponents are added; e.g., x² · x³ = x⁵ . Note that the base must be the same. When a quantity already containing an exponent is raised to a power, the exponents are multiplied; e.g., ( x² ) ³ = x⁶ .

ex·po·nent / ikˈspōnənt; ˈekspōnənt/ • n. 1. a person who believes in and promotes the truth or benefits of an idea or theory: an early exponent of the teachings of Thomas Aquinas. ∎  a person who has and demonstrates a particular skill, esp. to a high standard: he's the world's leading exponent of country rock guitar. 2. Math. a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g., 3 in 2³ = 2 × 2 × 2).

exponent Superscript number placed to the right of a symbol indicating its power, e.g. in a⁴ (=a × a × a × a), 4 is the exponent. Certain laws of exponents apply in mathematical operations. For example, 3² × 3³ = 3^{(2 + 3)} = 3⁵; 3⁴/3³ = 3^{(4 − 3)} = 3¹; (3²)³ = 3^{(2 × 3)} = 3⁶; 3⁻⁵ = 1/3⁵.

exponent interpreting XVI; sb. (math.) index of a power XVIII; expounder, interpreter XIX. — L. expōnēns, -ent-, prp. of expōnere EXPOUND.
So exponential (math.) XVIII. — F. exponentiel.

exponent See floating-point notation.

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