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Chapter 1

Sets and Numbers

 
1.3 Operations and Properties in the Set R - Continued

It is known from high school education the meaning of a power with an integer exponent.

If the number v is a positive integer greater than two we define:

 (v factors).

If v=1 : 

If v=0: 

In addition, .

The properties of the powers are summarized in the table bellow:
 
 
 
 
 
 
 
The following formulas must be reminded:

Also, it must be reminded that the square root of a non negative number a, denoted as  is the
non negative number whose second power is equal to a.

Finally the vth root of a non negative number a, denoted as  is the non negative number whose vth power is equal to a.

The following formulas are valid:

 At this point the powers with rational exponents can be defined.
Thus if a positive real number, m integer and n positive integer then:

  , while 

For example: