50 2. THE LIBRARY OF FUNCTIONS
2.2.1 POWERS AND ROOTS
e simplest notion of a power is that of repeated multiplication. If we multiply a number a by
itself m times, we get
a a a D a
m
We also adopt the convention that
1
a
D a
1
which means that the reciprocal of a number to a power is that number to the negative of the
power. ere are a number of rules about how powers interact, summarized in the following
Knowledge Box.
Knowledge Box 2.10
Algebraic Rules for Powers
• a
n
D
1
a
n
• a
n
a
m
D a
nCm
•
a
n
a
m
D a
nm
•
.
a
n
/
m
D a
nm
Example 2.25 is example showcases the rules for powers on a simple problem.
2
3
2
4
5
D
2
3C4
5
D
2
7
5
D 2
35
D 34; 359; 738; 368
e final step is probably not needed, as 2
35
is the same number and much easier to read.
˙
Definition 2.5 For a positive whole number n we define
b D
n
p
a
to be any number for which b
n
D a. Notice that, when n is even, there are two possibilities, ˙
n
p
a.
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