- NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers Ex 11.1
- NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers Ex 11.2
- NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers Ex 11.3
NCERT Solutions for Class 7 Maths Chapter 11 Exponents and Powers Ex 11.1 (Rationalised Contents)
Ex 11.1 Class 7 Maths Question 1.
Find the value of
(i) 26
(ii) 93
(iii) 112
(iv) 54
Solution:
(i) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64
(ii) 93 = 9 × 9 × 9 = 729
(iii) 112 = 11 × 11 = 121
(iv) 54 = 5 × 5 × 5 × 5 = 625
Ex 11.1 Class 7 Maths Question 2.
Express the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(iii) b × b × b × b
(iv) 5 × 5 × 7 × 7 × 7
(v) 2 × 2 × a × a
(vi) a × a × a × c × c × c × c × d
Solution:
(i) 6 × 6 × 6 × 6 = 64
(ii) t × t = t2
(iii) b × b × b × b = b4
(iv) 5 × 5 × 7 × 7 × 7 = 52 × 73
(v) 2 × 2 × a × a = 22 × a2 = (2a)2
(vi) a × a × a × c × c × c × c × d = a3 × c4 × d
Ex 11.1 Class 7 Maths Question 3.
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125
Solution:
Ex 11.1 Class 7 Maths Question 4.
Identify the greater number, wherever possible, in each of the following?
(i) 43 or 34
(ii) 53 or 35
(iii) 28 or 82
(iv) 1002 or 2100
(v) 210 or 102
Solution:
(i) 43 or 34
43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81
Since 81 > 64
∴ 34 > 43.
(ii) 53 or 35
53 = 5 × 5 × 5 = 125
35 = 3 × 3 × 3 × 3 × 3 = 243
Since 243 > 125
∴ 35 > 53.
(iii) 28 or 82
28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
82 = 8 × 8 = 64
Since 256 > 64
∴ 28 > 82.
(iv) 1002 or 2100
1002 = 100 × 100 = 10000
2100 = 2 × 2 × 2 × … 100 times
Here, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 214 = 16384
Since 16384 > 10000
∴ 2100 > 1002.
(v) 210 or 102
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
102 = 10 × 10 = 100
Since 1024 > 100
∴ 210 > 102.
Ex 11.1 Class 7 Maths Question 5.
Express each of the following as the product of powers of their prime factors.
(i) 648
(ii) 405
(iii) 540
(iv) 3,600
Solution:
Ex 11.1 Class 7 Maths Question 6.
Simplify:
(i) 2 × 103
(ii) 72 × 22
(iii) 23 × 5
(iv) 3 × 44
(v) 0 × 102
(vi) 52 × 33
(vii) 24 × 32
(viii) 32 × 104
Solution:
(i) 2 × 103 = 2 × 10 × 10 × 10 = = 2000
(ii) 72 × 22 = = 7 × 7 × 2 × 2 = 196
(iii) 23 × 5 = 2 × 2 × 2 × 5 = 40
(iv) 3 × 44 = 3 × 4 × 4 × 4 × 4 = 768
(v) 0 × 102 = 0 × 10 × 10 = 0
(vi) 52 × 33 = 5 × 5 × 3 × 3 × 3 = 675
(vii) 24 × 32 = 2 × 2 × 2 × 2 × 3 × 3 = 144
(viii) 32 × 104 = 3 × 3 × 10 × 10 × 10 × 10 = 90000
Ex 11.1 Class 7 Maths Question 7.
Simplify:
(i) (-4)3
(ii) (-3) × (-2)3
(iii) (-3)2 × (-5)2
(iv) (-2)3 × (-10)3
Solution:
(i) (-4)3 = (-4) × (-4) × (-4) = -64 [∵ (-a)odd number = -aodd number]
(ii) (-3) × (-2)3 = (-3) × (-2) × (-2) × (-2)
= (-3) × (-8) = 24
(iii) (-3)2 × (-5)2 = [(-3) × (-5)]2
= 152 = 225 [∵ am × bm = (ab)m]
(iv) (-2)3 × (-10)3 = [(-2) × (-10)]3
= 203 = 8000 [∵ am × bm = (ab)m]
Ex 11.1 Class 7 Maths Question 8.
Compare the following numbers:
(i) 2.7 × 1012; 1.5 × 108
(ii) 4 × 1014; 3 × 1017
Solution:
(i) 2.7 × 1012; 1.5 × 108
Here, 1012 > 108
∴ 2.7 × 1012 > 1.5 × 108
(ii) 4 × 1014; 3 × 1017
Here, 1017 > 1014
∴ 4 × 1014 < 3 × 1017
Related Links:
NCERT Solutions for Maths Class 8
NCERT Solutions for Maths Class 9
NCERT Solutions for Maths Class 10
NCERT Solutions for Maths Class 11