Posted on: October 27, 2021 Posted by: user Comments: 0

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 the exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125.
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 1
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 2
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 3

Question 4.

Identify wherever possible, in each of the following?
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 4
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 5
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 6

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:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 7
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 8
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 9
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 10

Question 6.
Simplify:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 11
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 12

Question 7.
Simplify:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 13
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 14
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 15

Question 8.
Compare the following numbers:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 16
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 17

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 :
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 18
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 19
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 20
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 21

Question 2.
Simplify and express each of the following in exponential form:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 22
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 23
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 24
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 25

Question 3.
Say true or false and justify your answer:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 26
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 27

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:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 28
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 29
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 30

Question 5.
Simplify
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 31
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 32
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 33

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:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 34
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 35

Question 2.
Find the number from each of the following expanded forms :
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 36
Solution:
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers 37
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.

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