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Definition: A number placed in a superscript position to the right of another number or variable to indicate repeated multiplication: a2 indicates a x a, a3 indicates a x a x a, etc. Sometimes ‘power’ is used instead of exponent; more strictly, power is the result of the multiplication - for instance, 4 is the second power of 2 (i.e. 22). If the exponent is negative then the expression is the reciprocal of the number with a positive value of the exponent: for example, x-n = 1/xn. Any number with an exponent of zero is equal to 1 (x0 = 1). Certain laws of exponents (laws of indices) apply: multiplication: anam = an+m; division: an/am = an-m; raising to a power: (an)m = anm. Fractional exponents are defined byam/n = n√(am).
Source: Nelson, David. The Penguin dictionary of mathematics 4th ed. London, New York. Penguin. 2008.