Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 10
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37MODULE -
1
Exponents and Radicals
Algebra
+
+
+
+
×
2
2
2
2
2
10
2
5
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
=
=
⎜
⎟
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
⎝
⎠
7
7
7
Notes
From the above two cases, we can infer the following:
Law 4:
If a is any non-zero rational number and m and n are two positive integers, then
( )
n
=
m
mn
a
a
Let us consider an example.
3
⎡
⎤
2
⎛
⎞
2
⎜
⎟
⎢
⎥
Example 2.12:
Find the value of
⎝
⎠
⎢
⎥
5
⎣
⎦
3
⎡
⎤
2
×
⎛
⎞
2
3
6
⎡
⎤
⎛
⎞
2
2
2
64
⎜
⎟
⎢
⎥
=
=
⎜
⎟
Solution:
=
⎢ ⎣
⎥ ⎦
⎝
⎠
⎢
⎥
5
⎝
⎠
⎣
⎦
5
5
15625
2.3.1 Zero Exponent
−
÷
=
Recall that
, if m > n
m
n
m
n
a
a
a
1
=
, if n > m
−
n
m
a
Let us consider the case, when m = n
∴
−
÷
=
m
m
m
m
a
a
a
m
a
⇒
=
0
a
m
a
⇒
=
0
1 a
Thus, we have another important law of exponents,.
o
Law 5:
If a is any rational number other than zero, then a
= 1.
Example
2.13:Find the value of
0
0
⎛ −
⎛
⎞
⎞
2
3
⎜
⎟
⎜
⎟
(i)
(ii)
⎝
⎠
⎝
⎠
7
4
0
⎛
⎞
2
⎜
⎟
0
Solution:
(i) Using a
= 1, we get
= 1
⎝
⎠
7
48
Mathematics Secondary Course
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