This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopędia. 16 volumes complete..
Exponent (Lat. erponere, to manifest), in arithmetic and algebra, a small figure or letter, written to the right of and above a quantity or algebraic term, to show how often the quantity or term must be taken as a factor. Thus, 34 (which is read the fourth power of 3," or 3, fourth power) signifies that 3 is to be taken as a factor four times, or multiplied into itself three times, as follows: 3x3 = 9; 3x9 =27; 3 x 27=81. In like manner (a + b)c signifies that the sum of the numbers represented by a and b must be multiplied consecutively into itself as many times less one as there are units in c. (See Algebra.)-Exponential equations and functions are those in which the exponents contain unknown or variable quantities; such as y=ax, in which a is the only known quantity. Exponential equations are usually reduced to logarithmic, and thus solved.
 
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