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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

1. Find the value of each of the following.
4
2 2
(a) (–1) 10 (b) (2) 5 (c) [(–3) ] (d) (–2) × (–2) 6
2. Simplify the following and write in exponential form.
2
(a) 10 × 100 (b) (–7) × (–7) × (–7) × (–7) × (–7)
(c) (–5) × 125 (d) 6 ÷ 3 3
3
3
3. Evaluate the following using laws of exponents.
2
3
18 × 9 × 4 3 8 ×( ) 4
3
2
2
(a) (b)
2
12 × 6 4 2 × 8
6
4. Express the following numbers in the standard form.
(a) 67,500,000,000 (b) 18,312,620,000,000,000 (c) 2210.735
5. Express the following numbers in usual form.
(a) 2.2 × 10 4 (b) 9.81 × 10 10 (c) 1.231 × 10 5
Exponents

We have learnt in the previous class that exponents are a powerful way to express repeated
multiplication of a number by itself in short form. For example,

Here, 2 is called the base and 10 is called
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 10 Exponent the exponent or index. We read 2 as
10
2 10 ‘2 raised to the power 10’ or ‘2 to the
Repeated multiplication of 2 by itself 10 times Base power 10’ or ‘tenth power of 2’.
Similarly, 1000000000 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10 , here the base is 10 and the
9
power or exponent is 9.

Life Skills

Let us discuss how Seema’s mother got the number of Seema’s ancestors (four generations back):

Seema

Mother Father

Mother Father Mother Father

Mother Father Mother Father Mother Father Mother Father

Mother Father Mother Father Mother Father Mother Father Mother Father Mother Father Mother Father Mother Father

Seema’s parents (Generation 1 back) = 2 1
Seema’s grandparents (Generation 2 back) = 2 2
Seema’s great-grandparents (Generation 3 back) = 2 3
Seema’s great-great-grandparents (Generation 4 back) = 2 4
3
4
Therefore, total number of ancestors (four generation back) = 2 + 2 + 2 + 2 = 2 + 4 + 8 + 16 = 30
1
2
Can you find how many ancestors are there in the 10th generation back?
263 Exponents and Powers