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:

, a,
b non negative numbers

, a
non negative, b positive
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:


.