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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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What does the exponent or power mean in math?
An integer exponent is the number of times that a number is multiplied by itself. For example: if the exponent of a is 3, then it represents the number a3 = a*a*a. The laws of exponents can be extended to arrive at definitions of negative exponents [a-3 = 1/a3] and fractional exponents [a1/3 is the cube or third root of a]. These definitions can be further extended to exponents that are irrational numbers, or even complex number.
When adding numbers with exponents do you add or subtract the exponents?
you do not do anything when you add numbers with exponents. you just figure out the answer. it is only if you multiply numbers with exponents, where you add the exponents..
When adding numbers with fraction exponents do you add the exponents?
Fractional exponents follow the same rules as integral exponents. Integral exponents are numbers raised to an integer power.
When you are multiplying exponents do you only add the exponents or do you also multiply the bases?
Add the exponents
How are the laws of rational exponents similar to laws of integer exponents?
The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
