Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 4
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37MODULE -
1
Exponents and Radicals
Algebra
Example 2.3:
Express each of the following in exponential notation and write the base
and exponent in each case.
125
Notes
(i) 4096
(ii)
(iii) – 512
729
12
Solution:
(i) 4096 = 4 × 4 × 4 × 4 × 4 × 4
Alternatively 4096 = (2)
6
= (4)
Base = 2, exponent =12
Here, base = 4 and exponent = 6
3
⎛
⎞
125
5
5
5
5
×
×
⎜
⎟
(ii)
=
=
⎝
⎠
729
9
9
9
9
⎛
⎞
5
⎜
⎟
Here, base =
and exponent = 3
⎝
⎠
9
9
(iii) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2
Here, base = 2 and exponent = 9
Example 2.4:
Simplify the following:
3
4
⎛
⎞
⎛
⎞
3
4
×
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
2
3
3
⎛
⎞
3
3
3
3
3
3
=
×
×
=
⎜
⎟
Solution:
⎝
⎠
3
2
2
2
2
2
4
⎛
⎞
4
4
4
=
⎜
⎟
Similarly
⎝
⎠
4
3
3
3
4
⎛
⎞
⎛
⎞
3
4
3
4
3
4
×
⎜
⎟
⎜
⎟
×
=
⎝
⎠
⎝
⎠
3
4
2
3
2
3
×
3
3
16
16
32
×
=
=
4
8
3
3
Example 2.5:
Write the reciprocal of each of the following and express them in exponential
form:
2
9
⎛
⎞
⎛
⎞
3
5
−
⎜
⎟
⎜
⎟
5
(i) 3
(ii)
(iii)
⎝
⎠
⎝
⎠
4
6
42
Mathematics Secondary Course
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