Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 3
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37MODULE -
1
Exponents and Radicals
Algebra
From the above, we say that
The notation for writing the product of a number by itself several times is called the
Exponential Notation or Exponential Form.
Notes
20
10
Thus, 5 × 5 × .... 20 times = 5
and (–7) × (–7) × .... 10 times = (–7)
20
In 5
, 5 is the base and exponent is 20.
10
In (–7)
, base is –7 and exponent is 10.
Similarly, exponential notation can be used to write precisely the product of a ratioinal
number by itself a number of times.
16
⎛
⎞
3
3
3
×
×
=
⎜
⎟
.........1
6
times
Thus,
⎝
⎠
5
5
5
10
⎛
⎞
⎛
⎞
⎛
⎞
1
1
1
−
× ⎟
−
× ⎟
=
⎜
⎜
⎜
⎟
..........
10
times
–
and
⎝
⎠
⎝
⎠
⎝
⎠
3
3
3
m
In general, if a is a rational number, multiplied by itself m times, it is written as a
.
Here again, a is called the base and m is called the exponent
Let us take some examples to illustrate the above discussion:
Example 2.1:
Evaluate each of the following:
3
4
⎛
⎞
⎛
⎞
2
3
( )
−
⎜
⎟
⎜
⎟
i
(ii)
⎝
⎠
⎝
⎠
7
5
( )
3
3
⎛
⎞
2
2
2
2
2
8
=
×
×
=
=
⎜
⎟
Solution:
(i)
( )
3
⎝
⎠
7
7
7
7
343
7
( )
4
−
4
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
3
3
3
81
−
=
−
−
−
−
=
=
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
(ii)
( )
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
5
5
5
5
5
5
625
5
Example 2.2:
Write the following in exponential form:
(i) (–5) × (–5) × (–5) × (–5) × (–5) × (–5) × (–5)
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
3
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
(ii)
×
×
×
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
11
11
11
11
7
Solution:
(i) (–5) × (–5) × (–5) × (–5) × (–5) × (–5) × (–5) = (–5)
4
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
3
3
3
3
3
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
(ii)
×
×
×
=
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
⎝
⎠
11
11
11
11
11
Mathematics Secondary Course
41
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