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NCERT Solutions for class 7 Maths chapter 13 – Exponents and Powers

Back Exercise

Exercise 13.1

Question 1.
Find the value of:

1. 2⁶
2. 9³
3. 11²
4. 5⁴.

Solution:

1. 2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
2. 9³ = 9 × 9 × 9 = 729
3. 11² = 11 × 11 = 121
4. 5⁴ = 5 × 5 × 5 × 5 = 625.

Question 2.
Express the following in exponential form:

1. 6 × 6 × 6 × 6
2. t × t
3. b × b × b × b
4. 5 × 5 × 7 × 7 × 7
5. 2 × 2 × a × a
6. a × a × a × c × c × c × c × d.

Solution:

1. 6 × 6 × 6 × 6 = 6⁴
2. t × t = t²
3. b × b × b × b = b⁴
4. 5 × 5 × 7 × 7 × 7 = 5² × 7³
5. 2 × 2 × a × a = 2² × a²
6. a × a × a × c × c × c × c × d = a³ × c⁴ × d.

Question 3.
Express each of the following numbers using the exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125.
Solution:




Question 4.
Identify wherever possible, in each of the following?

Solution:

Question 5.
Express each of the following as a product of powers of their prime factors:
(i) 648
(ii) 405
(iii) 540
(iv) 3600
Solution:

Question 6.
Simplify:

Solution:

Question 7.
Simplify:

Solution:

Question 8.
Compare the following numbers:

Solution:

Exercise 13.2

Question 1.
Using laws of exponents, simplify and write the answer in exponential form :

Solution:

Question 2.
Simplify and express each of the following in exponential form:

Solution:

Solution:

Question 4.
Express each of the following as a product of prime factors only in exponential form:
(i) 108 × 192
(ii) 270
(iii) 729 × 64
(iv) 768.
Solution:

Question 5.
Simplify

Solution:

Exercise 13.3

Question 1.
Write the following numbers in the expand forms :
(i) 279404
(ii) 3006194
(iii) 2806196
(iv) 120719
(v) 20068.
Solution:

Question 2.
Find the number from each of the following expanded forms :

Solution:

Question 3.
Express the following numbers in standard form:

1. 5,00,00,000
2. 70,00,000
3. 3,18,65,00,000
4. 3,90,878
5. 39087.8
6. 3908.78

Solution:

1. 5,00,00,000 = 5 × 10⁷
2. 70,00,000 = 7 × 10⁶
3. 3,18,65,00,000 = 3.1865 × 10⁹
4. 3,90,878 = 3.90878 × 10⁵
5. 39087.8 = 3.90878 × 10⁴
6. 3908.78 = 3.90878 × 10³

Question 4.
Express the number appearing in the following statements in standard form :

1. The distance between Earth and Moon is 384,000,000 m.
2. The speed of light in a vacuum is 300,000,000 miles.
3. The diameter of the Earth is 1,27,56,000 m.
4. Diameter of the Sun is 1,400,000,000 m.
5. In a galaxy, there are on average 100,000,000,000 stars.
6. The universe is estimated to be about 12,000,000,000 years old.
7. The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
8. 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
9. The earth has 1,353,000,000 cubic km of seawater.
10. The population of India was about 1,027,000,000 in March 2001.

Solution:

1. The mean distance between Earth and Moon is 3.84 × 10⁸ m.
2. The speed of light in a vacuum is 3 × 10⁸ m/s.
3. The diameter of the Earth is 1.2756 × 10⁷ m.
4. The diameter of the Sun is 1.4 × 10⁹ m.
5. In a galaxy, there are on average 1 × 10¹¹ stars.
6. The universe is estimated to be about 1.2 × 10¹⁰ years old.
7. The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 3 × 10²⁰ m.
8. 6.023 × 10²² molecules are contained in a drop of water weighing 1.8 gm.
9. The earth has 1.353 × 10⁹ cubic km of seawater.
10. The population of India was about 1.027 × 10⁹ in March 2001.