# Chapter 13 Exponents and Powers

Chapter 13 Exponents and Powers

Exercise 13.1
Ex 13.1 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 13.1 Class 7 Maths

Question 2.
Exress 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 = 63
(ii) t × t = t2
(iii) b × b × b × b = b4
(iv) 5 × 5× 7 × 7 × 7 = 52 × 73 = 52 · 73
(v) 2 × 2 × a × a = 22 × a2 = 22 · a2
(vi) a × a ×a × c × c × c × c × d = a3 × c4 × d = a3 · c4 · d

Ex 13.1 Class 7 Maths

Question 3.
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125

Solution:

Ex 13.1 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 is greater than 43.

(ii) 53 or 35
53 = 5 × 5 × 5 = 125
35 = 3 × 3 × 3 × 3 × 3 = 243
Since 243 > 125
35 is greater than 53.

(iii) 28 or 82
28 =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
82 = 8 × 8 = 64
Since 256 > 64
28 is greater than 28.

(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 > 10,000
2100 is greater than 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 is greater than 102.

Ex 13.1 Class 7 Maths

Question 5.
Express each of the following as the product of powers of their prime
(i) 648
(ii) 405
(iii) 540
(iv) 3600

Solution:

Ex 13.1 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 13.1 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)2 = (-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
= 202 = 8000 [
am × bm = (ab)m]

Ex 13.1 Class 7 Maths

Question 8.
Compare the following:
(i) 2.7 × 1012; 1.5 × 108
(ii) 4 × 1014; 3 × 1014

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