Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 8
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37MODULE -
1
Exponents and Radicals
Algebra
⎛
⎞
3
3
3
3
3
3
3
=
×
×
×
×
×
×
⎜
⎟
⎝
⎠
4
4
4
4
4
4
4
Notes
+
7
3
4
⎛
⎞
⎛
⎞
3
3
=
⎜
⎟
⎜
⎟
=
⎝
⎠
⎝
⎠
4
4
3
4
7
3+4
(iv) a
× a
= (a × a × a) × (a × a × a × a) = a
= a
From the above examples, we observe that
Law 1:
If a is any non-zero rational number and m and n are two positive integers, then
m
n
m+n
a
× a
= a
3
5
⎛
⎞
⎛
⎞
3
3
−
×
−
⎜
⎟
⎜
⎟
Example 2.8:
Evaluate
.
⎝
⎠
⎝
⎠
2
2
3
− , m = 3 and n = 5.
Solution:
Here a =
2
+
3
5
3
5
8
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
3
6561
−
×
−
−
=
−
=
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
∴
=
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
2
2
2
2
256
Example 2.9:
Find the value of
2
3
⎛
⎞
⎛
⎞
7
7
×
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
4
4
Solution:
As before,
+
2
3
2
3
5
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
7
7
7
7
16807
×
=
=
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
=
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
4
4
4
4
1024
Now study the following:
×
×
×
×
5
7
7
7
7
7
7
−
=
=
×
=
=
÷ 7
2
5
3
5
3
7
7
7
7
(i) 7
=
×
×
3
7
7
7
7
( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
−
7
−
×
−
×
−
×
−
×
−
×
−
×
−
3
3
3
3
3
3
3
3
=
÷ (–3)
7
4
(ii) (–3)
=
( ) ( ) ( ) ( )
( )
−
×
−
×
−
×
−
−
4
3
3
3
3
3
( )( )( ) ( )
−
−
−
=
−
3
7– 4
=
= (–3)
3
3
3
3
46
Mathematics Secondary Course
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