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NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1

CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.1 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.

Class 7 Maths NCERT Solutions Chapter 13 Exponents and Powers Ex 13.1

Question 1.
Find the value of:

(i) 26
Solution:
26 = 2 × 2 × 2 × 2 × 2 × 2 = 64

(ii) 93
Solution:
92 = 9 × 9 × 9 = 729

(iii) 112
Solution:
112 = 11 × 11 = 121

(iv) 54
Solution:
54 = 5 × 5 × 5 × 5 = 625

Question 2.
Express the following in exponential form :

(i) 6 × 6 × 6 × 6
Solution:
6 × 6 × 6 × 6 = 64

(ii) t x t
Solution:
t × t = t2

(iii) b × b × b × b
Solution:
b × b × b × b = b4

(iv) 5 × 5 × 7 × 7 × 7
Solution:
5 × 5 × 7 × 7 × 7 = 52 × 73

(v) 2 × 2 × a × a
Solution:
2 × 2 × a × a = 22 × a2

(vi) a × a × a × c × c × c × c × d
Solution:
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
Solution:
We have
NCERT Solutions for Class 7 maths Algebraic Expreesions img 29

(ii) 343
Solution:
We have
NCERT Solutions for Class 7 maths Algebraic Expreesions img 30

(iii) 729
Solution:
We have
NCERT Solutions for Class 7 maths Algebraic Expreesions img 31

(vi) 3125
Solution:
We have
NCERT Solutions for Class 7 maths Algebraic Expreesions img 32

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

(i) 43 or 34
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 38

(ii) 53 or 35
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 34

(iii) 28 or 82
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 35

(iv) 1002 or 2100
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 36

(v) 210 or 102
Solution:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 37

Question 5.
Express each of the following as a product of powers of their prime factors:

(i) 648
Solution:
To determine the prime factorization of 648, we use the division method, as shown below:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 25

(ii) 405
Solution:
We use the division method as shown under:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 26

(iii) 540
Solution:
We use the division method as shown under:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 27

(iv) 3600
Solution:
We use the division method as shown under:
NCERT Solutions for Class 7 maths Algebraic Expreesions img 28

Question 6.
Simplify:

(i) 2 × 103
Solution:
2 × 103 = 2 × 1000 = 2000

(ii) 72 x 22
Solution:
72 × 22 = (7 × 2)2 = (14)3 = 14 × 14 = 196

(iii) 23 × 5
Solution:
23 × 5 = 2 × 2 × 2 × 5
= 8 × 5 = 40

(iv) 3 × 44
Solution:
3 × 44 = 3 × 4 × 4 × 4 × 4
= 3 × 256 = 768

(v) 0 × 102
Solution:
0 × 102 = 0

(vi) 52 × 33
Solution:
52 × 33 = 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675

(vii) 24 × 32
Solution:
24 × 32 = 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144

(viii) 32 × 104
Solution:
32 × 104 = 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000

Question 7.
Simplify:

(i) (-4)3
Solution:
(- 4)3 = (- 4) × (- 4) × (- 4) = – 64

(ii) (-3) × (-2)3
Solution:
(-3) × (-2)3 = (-3) × (- 2) × (- 2) × (- 2) = (- 3) × (- 8) = 24

(iii) (- 3)2 × (- 5)2
Solution:
(- 3)2 × (- 5)2 = (- 3) × (- 3) × (- 5) × (- 5) = 9 × 25 = 225

(iv) (-2)3 × (-10)2
Solution:
(-2)3 × (-10)3 = (-2) × (-2) × (-2) x (-10) × (-10) × (-10) = (-8) × (-1000) = 8000

Question 8.
Compare the following numbers:

(i) 2.7 × 1012 ; 1.5 × 108
Solution:
We have,
2.7 × 1012 = 2.7 × 10 × 1011
= 27 × 1011, contains 13 digits and 1.5 × 108 = 1.5 × 10 × 107
= 15 × 107 contains 9 digits
Clearly, 2.7 × 1012 > 1.5 × 108

(ii) 4 × 1014; 3 × 1017
Solution:
We have, 4 × 1014, contains 15 digits and, 3 × 1017, contains 18 digits 4 × 1014 < 3 × 1017

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