Module-1 Algebra - Mathematics Secondary Course - Exponents And Radicals Worksheet Page 6
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37MODULE -
1
Exponents and Radicals
Algebra
8
⎛
⎞
2
−
⎜
⎟
5
4
(i) (–3)
(ii) (7)
(iii)
⎝
⎠
11
Notes
3. Evaluate each of the following
4
4
3
⎛
⎞
⎛
⎞
⎛
⎞
3
–
2
3
⎜
⎟
⎜
⎟
⎜
⎟
(i)
(ii)
(iii)
–
⎝
⎠
⎝
⎠
⎝
⎠
7
9
4
4. Simplify the following:
5
6
⎛
⎞
⎛
⎞
7
3
×
⎜
⎟
⎜
⎟
(i)
⎝
⎠
⎝
⎠
3
7
2
2
⎛
⎞
⎛
⎞
5
3
−
÷
−
⎜
⎟
⎜
⎟
(ii)
⎝
⎠
⎝
⎠
6
5
5. Find the reciprocal of each of the following:
4
⎛
⎞
3
−
⎜
⎟
5
4
(i) 3
(ii) (–7)
(iii)
⎝
⎠
5
2.2 PRIME FACTORISATION
Recall that any composite number can be expressed as a product of prime numbers. Let
us take the composite numbers 72, 760 and 7623.
2 72
(i) 72 = 2 × 2 × 2 × 3 × 3
2 36
2 760
3
2
2 18
= 2
× 3
2 380
3 9
(ii) 760 = 2 × 2 × 2 × 5 × 19
2 190
3
3 7623
5 95
3
1
1
= 2
× 5
×19
3 2541
19
(iii) 7623 = 3 × 3 × 7 × 11 ×11
7 847
11 121
2
1
2
= 3
× 7
× 11
11
We can see that any natural number, other than 1, can be expressed as a product of
powers of prime numbers in a unique manner, apart from the order of occurrence of
factors. Let us consider some examples
Example 2.6:
Express 24300 in exponential form.
Solution:
24300 = 3 × 3 × 3 × 3 × 2 × 2 × 5 × 5 × 3
44
Mathematics Secondary Course
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education