Negative and Fractional Powers
Negative Powers
The question now arises as to what we mean by a negative
power. To interpret this note that
If rule 2 is to apply, then a 2 ÷ a 5 =
a 2 - 5 = a 3. Thus, a - 3 = 1 /
a 3
The general rule is:
Fractional Powers
If a is a positive number, then the square root of a
is the number which, multiplied by itself, gives a: Thus 3 is the
square root of 9 since 3 2 = 9: We write  . Note that, by definition,
 . This gives us a way of
interpreting  for, by rule 1,
so that  The general rule is
that, if a is a positive number and n is a positive integer, then
where  is the n-th
root of a. We can see this in general for, by rule 3,
|