NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers.

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 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 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:

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 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:

Question 3.
Say true or false and justify your answer :

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:

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 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 :

(a) The distance between Earth and Moon is 384,000,000 m.
(b) Speed of light in vacuum is 300,000,000 mis.
(c) Diameter of the Earth is 1,27,56,000 m.
(d) Diameter of the Sun is 1,400,000,000 m.
(e) In a galaxy there are on an average 100,000,000,000 stars.
(f) The universe is estimated to be about 12,000,000,000 years old.
(g) The distance of Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
(i) The earth has 1,353,000,000 cubic km of sea water.
(j) The population of India was about 1,027,000,000 in March, 2001.

Solution:

(a) The mean distance between Earth and Moon is 3.84 × 10⁸ m.
(b) Speed of light in vacuum is 3 × 10⁸ m/s.
(c) Diameter of the Earth is 1.2756 × 10⁷ m.
(d) Diameter of the Sun is 1.4 × 10⁹ m.
(e) In a galaxy there are on an average 1 × 10¹¹ stars.
(f) The universe is estimated to be about 1.2 × 10¹⁰ years old.
(g) The distance of Sun from the centre of the Milky Way Galaxy is estimated to be 3 × 10²⁰ m.
(h) 6.023 × 10²² molecules are contained in a drop of water weighing 1.8 gm.
(i) The earth has 1.353 × 10⁹ cubic km of sea water.
(j) The population of India was about 1.027 × 10⁹ in March, 2001.

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers MCQ

Important Multiple Choice Questions

1. The exponential form of 10000 is

(a) 10³
(b) 10⁴
(c) 10⁵
(d) none of these.

2. The exponential form of 100000 is

(a) 10³
(b) 10⁴
(c) 10⁵
(d) none of these.

3. The exponential form of 81 is

(a) 3⁴
(b) 3³
(c) 3²
(d) none of these.

4. The exponential form of 125 is

(a) 5⁴
(b) 5³
(c) 5²
(d) none of these.

5. The exponential form of 32 is

(a) 2³
(b) 2⁴
(c) 2⁵
(d) none of these.

6. The exponential form of 243 is

(a) 3⁵
(b) 3⁴
(c) 3³
(d) 3².

7. The exponential form of 64 is

(a) 2⁵
(b) 2⁶
(c) 2⁷
(d) 2⁸.

8. The exponential form of 625 is

(a) 5²
(b) 5³
(c) 5⁴
(d) 5⁵.

9. The exponential form of 1000 is

(a) 10¹
(b) 10²
(c) 10³
(d) 10⁴.

10. The value of (- 2)³ is

(a) 8
(b) – 8
(c) 16
(d) – 16.

11. The value of (- 2)⁴ is

(a) 8
(b) – 8
(c) 16
(d) – 16.

12. What is the base in 82?

(a) 8
(b) 2
(c) 6
(d) 10.

13. What is the exponent in 82?

(a) 8
(b) 2
(c) 16
(d) 6.

14. (-1)^{even number} =

(a) -1
(b) 1
(c) 0
(d) none of these

16. 0 × 10⁴ =

(a) 0
(b) 10⁴
(c) 1
(d) none of these.

17. If 2³ × 2⁴ = 2^?, then ? =

(a) 3
(b) 4
(c) 1
(d) 7.

18. If (- 3)⁴ × (- 3)⁶ = (- 3)^?, then ? =

(a) 4
(b) 10
(c) 6
(d) 12.

19. 2⁷ ÷ 2³ =

(a) 2⁴
(b) 2¹⁰
(d) 2
(d) \(\frac { 1 }{ 2 } \)

20. 10⁶ ÷ 10⁵ =

(a) 10¹
(b) 10⁵
(c) 10⁶
(d) 10¹¹.

21. b × b × b × b × b =

(a) b⁵
(b) b⁴
(c) b⁶
(d) b³.

22. (- 5)⁴ =

(a) 125
(b) 625
(c) 375
(d) 125.

23. a^m × aⁿ =

(a) a^m+n
(b) a^m-n
(c) a^mn
(d) a^m/n

24. am ÷ an =

(a) a^m+n
(b) a^m-n
(c) a^mn
(d) a^m/n

25. (2²)³ =

(a) 2²
(b) 2³
(c) 2¹
(d) 2⁶.

26. (5²)¹⁰ =

(a) 5²
(b) 5²⁰
(c) 5¹⁰
(d) 5⁵.

27. (a^m)ⁿ =

(a) a^m+n
(b) a^m-n
(c) a^mn
(d) a^m/n.

28. If a is any non-zero integer, then a° =

(a) a
(b) 0
(c) 1
(d) none of these.

29. 3° =

(a) 0
(b) 1
(c) 3
(d) none of these.

30. 3° × 4° × 5° =

(a) 1
(b) 3
(c) 4
(d) 5.

31. (2° + 3°) × 4° =

(a) 1
(b) 2
(c) 3
(d) 4.

32. 3° + 4° + 5° =

(a) 1
(b) 2
(c) 3
(d) none of these.

33. Which of the following is true?

(a) 2° = (100)°
(b) 10² × 10⁸ = 10¹⁶
(c) 2² × 3³ = 65
(d) 2³ > 3².

34. (2² × 2)² =

(a) 2³
(b) 2⁴
(c) 2⁵
(d) 2⁶.

35. \(\frac { { 3 }^{ 8 } }{ { 3 }^{ 5 }\times { 3 }^{ 3 } } =\)

(a) 1
(b) 3
(c) 5
(d) 8

36. (\(\frac { { a }^{ 4 } }{ { a }^{ 2 } } \times { a }^{ 3 }=\))

(a) a⁴
(b) a⁵
(c) a⁶
(d) a⁸.

37. 82 ÷ 24 =

(a) 1
(b) 2
(c) 3
(d) 4

38. (-2a)³ =

(a) 2a³
(b) 4a³
(c) 8a³
(d) -8a³

39. a^m ÷ b^m =

(a) a^m b^m
(b) (\(\frac { a }{ b } \))^m
(c) \(\frac { a }{ b } \)
(d) 1

40. (ab)^m =

(a) a^m b^m
(b) a^mb
(c) ab^m
(d) ab

41. 333 in standard form is

(a) 3.33 × 10²
(b) 3.33 × 10³
(c) 3.33 × 10¹
(d) 3.33 × 10⁴.

42. 6000 in standard form is

(a) 6 × 10³
(b) 6 × 10⁶
(c) 6 × 10⁴
(d) 6 × 10⁵.

43. 3430000 in standard form is

(a) 3.43 × 10⁶
(b) 3.43 × 10⁴
(c) 3.43 × 10²
(d) 3.43 × 10¹⁰.

44. 1353000000 in standard form is

(a) 1.353 × 10⁹
(b) 1.353 × 10⁶
(c) 1.353 × 10³
(d) 1.353 × 10¹².

45. 100000000000 in standard form is

(a) 1 × 10⁸
(b) 1 × 10⁹
(c) 1 × 10¹⁰
(d) 1 × 10¹¹.

ANSWERS

HINTS/SOLUTIONS

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