Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 9

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MODULE -
1
Exponents and Radicals
Algebra
From the above, we can see that
Law 2:
If a is any non-zero rational number and m and n are positive integers (m > n), then
÷ a
m
n
m–n
a
= a
Notes
16
13
⎛
⎞
⎛
⎞
35
35
÷
⎜
⎟
⎜
⎟
Example 2.10:
Find the value of
.
⎝
⎠
⎝
⎠
25
25
16
13
⎛
⎞
⎛
⎞
35
35
÷
⎜
⎟
⎜
⎟
Solution:
⎝
⎠
⎝
⎠
25
25
−
16
13
3
3
⎛
⎞
⎛
⎞
⎛
⎞
35
35
7
343
=
=
=
⎜
⎟
⎜
⎟
⎜
⎟
=
⎝
⎠
⎝
⎠
⎝
⎠
25
25
5
125
In Law 2, m < n ⇒ n > m,
1
(
)
−
−
÷
=
=
m
n
n
m
a
a
a
then
−
m
n
a
Law 3:
When n > m
1
÷
=
m
n
a
a
−
m
n
a
6
9
⎛
⎞
⎛
⎞
3
3
÷
⎜
⎟
⎜
⎟
Example 2.11:
Find the value of
⎝
⎠
⎝
⎠
7
7
3
Solution:
Here a =
, m = 6 and n = 9.
7
1
6
9
⎛
⎞
⎛
⎞
⎛
⎞
3
3
−
3
9
6
÷
⎜
⎟
⎜
⎟
∴
⎜
⎟
=
⎝
⎠
⎝
⎠
7
7
⎝
⎠
7
3
7
343
=
=
3
3
27
Let us consider the following:
( )
2
+
×
=
×
=
=
=
(i)
3
3
3
3
3
6
3
2
3
3
3
3
3
3
5
⎡
⎤
2
2
2
2
2
2
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
3
3
3
=
×
×
×
×
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎢
⎥
(ii)
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎢
⎥
7
7
7
7
7
7
⎣
⎦
Mathematics Secondary Course
47

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