exponent (redirected from Exponents)

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., 2⁵=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 nth root, respectively, of the base. Any nonzero quantity raised to the zero power equals one; e.g., x⁰=5⁰=(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.

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The number written above the line and to the right of a number that indicates the power of a number. For example, 14 to the 4th power is actually 14 multiplied by itself four times. Sometimes, the exponent naturally indicates the number of zeros. For example, 10 to the 3rd power reflects three zeros. The number 467,000 can be stated as 467 x 10 to the 3rd. On a screen or printout, that number is expressed as 467E3. See floating point.

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(programming)

exponent - (Or "characteristic") The part of a floating-point number specifying the power of ten by which the mantissa should be multiplied. In the common notation, e.g. 3.1E8, the exponent is 8.