# MP Board Class 7th Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

## MP Board Class 7th Maths Solutions Chapter 13 Exponents and Powers Ex 13.1

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

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
(vi) 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:
(i) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29
(ii) 343 = 7 × 7 × 7 = 73
(iii) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36
(iv) 3125 = 5 × 5 × 5 × 5 × 5 = 55

Question 4.
Identify the greater number, wherever possible, in each of the following?
(i) 43 or 34
(ii) 53 or 35
(iii) 25 or 82
(iv) 1002 or 2100
(v) 210 or 1002
Solution:
(i) 43 = 4 × 4 × 4 = 64 and 34 = 3 × 3 × 3 × 3 = 81
As 81 > 64, therefore 34 > 43

(ii) 53 = 5 × 5 × 5 = 125,
35 = 3 × 3 × 3 × 3 × 3 = 243
As 243 > 125, therefore, 35 > 53

(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256,
82 = 8 × 8 = 64
As 256 > 64, therefore, 28 > 82

(iv) 2100 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
⇒ 2100 = (210)10 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 ×1024 × 1024 × 1024 = (1024)10
and 1002 = 100 × 100 = 10000
As (1024)10 > 10000, therefore 2100 > 1002

(v) 210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
and 102 = 10 × 10 = 100
As 1024 > 100, therefore 210 > 102

Question 5.
Express each of the following as product of powers of their prime factors:
(i) 648
(ii) 405
(iii) 540
(iv) 3600
Solution:
(i) 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23 × 34
(ii) 405 = 3 × 3 × 3 × 3 × 5 = 34 ×5
(iii) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 33 × 5
(iv) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24 × 32 × 52

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 = 2 × 1000 = 2000
(ii) 72 × 22 = 7 × 7 × 2 × 2 = 49 × 4 = 196
(iii) 23 × 5 = 2 × 2 × 2 × 5 = 8 × 5 = 40
(iv) 3 × 44 = 3 × 4 × 4 × 4 × 4 = 3 × 256 = 768
(v) 0 × 102 = 0 × 10 × 10 = 0
(vi) 52 × 33 = 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675
(vii) 24 × 34 = 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144
(viii) 32 × 104 = 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000 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
(ii) (-3) × (-2)3 = (-3) × (-2) × (-2) × (-2) = (-3) × (-8) = 24
(iii) (-3)2 × (-5)2 = (-3) × (-3) × (-5) × (-5) = 9 × 25 = 225
(iv) (-2)3 × (-10)3 = (-2) × (-2) × (-2) × (-10) × (-10) × (-10) = (-8) × (-1000) = 8000

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
Since, 1012 > 108
∴ 2.7 × 1012 > 1.5 × 108
(ii) 4 × 1014; 3 × 1017
Since, 1014 < 1017
∴ 4 × 1014 < 3 × 1017