Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 12
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37MODULE -
1
Exponents and Radicals
Algebra
2.4 NEGATIVE INTEGERS AS EXPONENTS
1
–1
i) We know that the reciprocal of 5 is
. We write it as 5
and read it as 5 raised to
Notes
5
power –1.
1
− . We write it as (–7)
–1
ii) The reciprocal of (–7) is
and read it as (–7) raised to the
7
power –1.
1
2
–2
iii) The reciprocal of 5
=
. We write it as 5
and read it as ‘5 raised to the power (–2)’.
2
5
From the above all, we get
m
If a is any non-zero rational number and m is any positive integer, then the reciprocal of a
⎛
⎞
1
⎜
⎟
e i
. .
–m
is written as a
and is read as ‘a raised to the power (–m)’. Therefore,
⎝
m
⎠
a
1
−
=
m
a
m
a
Let us consider an example.
Example 2.14:
Rewrite each of the following with a positive exponent:
−
−
2
7
⎛
⎞
⎛
⎞
3
4
−
⎜
⎟
⎜
⎟
(i)
(ii)
⎝
⎠
⎝
⎠
8
7
Solution:
−
2
2
⎛
⎞
⎛
⎞
2
3
1
1
8
8
=
=
=
=
⎜
⎟
⎜
⎟
(i)
2
2
2
⎝
⎠
⎝
⎠
⎛
⎞
8
3
3
3
3
⎜
⎟
2
⎝
⎠
8
8
−
7
7
⎛
⎞
⎛
⎞
7
4
1
7
7
−
=
=
=
−
⎜
⎟
⎜
⎟
(ii)
( )
7
−
7
⎝
⎠
⎝
⎠
⎛
⎞
7
4
4
4
−
⎜
⎟
⎝
⎠
7
From the above example, we get the following result:
p
If
is any non-zero rational number and m is any positive integer, then
q
−
m
m
⎛
⎞
⎛
⎞
m
p
q
q
⎜ ⎜
⎟ ⎟
=
=
⎜ ⎜
⎟ ⎟
.
m
⎝
q
⎠
p
⎝
p
⎠
50
Mathematics Secondary Course
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education