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\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Knowledge Desk
Exponential Spread: Suppose Rohit has 100 connections on a social media Swachh Bharat
network.
He is passionate about cleanliness and uploaded an inspiring social awareness
message about
Swachh Bharat. Every one of his 100 connections watches the video and shares
it with 2 new people who are not in his network, within 2 hours.
These new viewers then share the video with 2 more people, and this process
continues.
If this sharing pattern persists every 2 hours, can you calculate the total number
of views after 24 hours?

Practice Time 4B

1. Simplify and express the result in exponential form:

4
2 3
15
3
(a) 3 × 3 × 3 7 (b) (–100) ÷ (–100) 10 (c) (7 ) × 7 5
5 3
4
2
4
5
(d) x × y (e) (10 ) ÷ 10 4 (f) (3 ÷ 3 ) × 4 3

2
2
2 + 3 0     −   2  2
0
2
2
(g) (5 × 7 ) ÷ 35 2 (h) (i)      
3 2     3    
 
2. Simplify the following by using suitable laws of exponents:
(a) (3 ) × (–2) 2 (b) (2 × 3 ) × 6 2 (c) (a ÷ a ) × a 8
4
3
2 3
5
2
3
4
5 × 5 2 3 × 2 3
2
2
(d) (e) (f) (3 + 2 + 3) × (3 + 3 )
0
0
15 2 2 × 3
2 3
8
2
0
(g) (a × 2 ) ÷ (4 × a) (h) (4 + 1 ) × (–2) 0 (i) ((4 ) × 4 ) ÷ 4 8
0
4
4
3. Evaluate the following by using suitable exponential laws:
3
2
2
5 × 10 × 3 5 7 ×( ) 5 a × 5 4
2
8
5
(a) (b) (c)
6 × 5 7 2 × 7 10 × a 4
6
3
5
53
32 × a 4 ab × 2 8 3 × 2 × 2 2
4
3
3
×
(d) (e) (f)
32
2
10 × a 3 32 × ab 32 5
×
2
32
2
3
2
2
7 × 3 × 11 8 −3ab 2 × 8ab − ( 2ab ) × ab
(g) (h) (i)
11 ×× (2ab ) 2 − ( 3ab ) 3
73
3
2
2
8
4. By what number should (–3) be multiplied so that the product is equal to (9) ?
6
6
5. By what number should (–12) be divided so that the quotient is equal to 144?
6. Arrange the following in descending order:
3 5
2 2 + 3 , (2 ) , 2 × 2 , , 3 × 3 and 2 × 5 2
3
2
0
2 3
2
3 2
Mathematics-7 90