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In the number x, with positive integer exponent a, a is the number of times that 1 (not the number itself) is multiplied by x. So, for example in the expression, 43 the exponent is 3 and the number represented is "1 is multiplied by 4 three times". If you multiply 4 by itself 3 times, you will get 4*4 (one time) * 4 (two times) *4 (three times) and that is NOT 43: it is just a wrong description.

The laws of exponents are:

xa * xb = xa+b

xa / xb = xa-b

(xa)b = xa*b

(xy)a = xa * ya


The first three are used to extend the domain of exponents to negative integers and rational numbers. Exponents to Irrational Numbers are defined as limits of the exponents of the rational sequences converging to the irrational number.


Finally, 00 is not defined (because it does not converge).

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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

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Q: What is the definitions for exponents?
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