## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Ex 4.1

Question 1.
Fill in the blanks:
(i) In the expression 37, base = …….. and exponent = ……..
(ii) In the expression (-7)5, base = ………. and exponent = …….
(iii) In the expression $$\left( \frac { 2 }{ 5 } \right) ^{ 11 }$$, base = …… and exponent = …….
(iv) If base is 6 and exponent is 8, then exponential form = ……..
Solution:
(i) In the expression 37, base = 3 and exponent = 7.
(ii) In the expression (-7)5, base = -7 and exponent = 5.
(iii) In the expression $$\left( \frac { 2 }{ 5 } \right) ^{ 11 }$$, base = -7 and exponent = 11.
(iv) If base is 6 and exponent is 8, then exponential form = 68.

Question 2.
Find the value of the following:
(i) 26
(ii) 55
(v) (-6)4
(vi) $$\left( \frac { 2 }{ 3 } \right) ^{ 4 }$$
(v) $$\left( \frac { -2 }{ 3 } \right) ^{ 5 }$$
(vi) (-2)9
Solution:
(i) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64
(ii) 55 = 5 × 5 × 5 × 5 × 5 = 3125
(iii) (-6)4 = (-6) × (-6) × (-6) × (-6) = 1296

(vi) (-2)9 = (-2) × (-2) × (-2) × (-2) × (-2) × (-2) × (-2) × (-2) × (-2) = -512

Question 3.
Express the following in the exponential form:
(i) 6 × 6 × 6 × 6 × 6
(ii) t × t × t
(iii) 2 × 2 × a × a × a × a
(iv) a × a × a × c × c × c × c × d
Solution:
(i) 6 × 6 × 6 × 6 × 6 = 65
(ii) t × t × t = t3
(iii) 2 × 2 × a × a × a × a = 22 × a4 = 22a4
(iv) a × a × a × c × c × c × c × d = a3 × c4 × d = a3c4d

Question 4.
Simplify the following:
(i) 7 × 103
(ii) 25 × 9
(iii) 33 × 104
Solution:
(i) 7 x 103 = 7 × 10 × 10 × 10 = 7 × 1000 = 7000
(ii) 25 × 9 = 2 × 2 × 2 × 2 × 2 × 9 = 32 × 9 = 288
(iii) 33 × 104 = 3 × 3 × 3 × 10 × 10 × 10 × 10 = 27 × 10000 = 270000

Question 5.
Simplify the following:
(i) (-3) × (-2)3
(ii) (-3)2 × (-5)2
(iii) (-2)3 × (-10)4
(iv) (-1)9
(v) 252 × (-1)31
(vi) 42 × 33 × (-1)122
Solution:
(i) (-3) × (-2)3 = (-3) × (-2) × (-2) × (-2) = 24
(ii) (-3)2 × (-5)2 = (-3) × (-3) × (-5) × (-5) = 9 × 25 = 225
(iii) (-2)3 × (-10)4 = (-2) × (-2) × (-2) × 10 × 10 × 10 × 10 = -8 × 10000 = -80000
(iv) (-1)9 = -1 (∵ 9 is odd)
(v) 252 × (-1)31 = 25 × 25 × (-1) (∵ 31 is odd)
= 625 × (-1) = -625
(vi) 42 × 33 × (-1)122
= 4 × 4 × 3 × 3 × (1) = 144 × 1 = 144 (∵ 122 is even)

Question 6.
Identify the greater number in each of the following:
(i) 43 or 34
(ii) 73 or 37
(iii) 45 or 54
(iv) 210 or 102
Solution:
(i) 43 or 34
43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81
34 is greater
(ii) 73 or 33
73 = 7 × 7 × 7 = 343
37 = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187
37 is greater
(iii) 45 or 54
45 = 4 × 4 × 4 × 4 × 4 = 1024
54 = 5 × 5 × 5 × 5 = 625
45 is greater
(iv) 210 or 102
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
102 = 10 × 10 = 100
210 is greater

Question 7.
Write the following numbers as powers of 2:
(i) 8
(ii) 128
(iii) 1024
Solution:
(i) 8 = 2 × 2 × 2 = 23
(ii) 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 27

(iii) 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 210

Question 8.
To what power (-2) should be raised to get 16?
Solution:
16 = (-2) × (-2) × (-2) × (-2) = (-2)4
Power = 4

Question 9.
Write the following numbers as powers of (-3):
(i) 9
(ii) -27
(iii) 81
Solution:
(i) 9 = (-3) × (-3) = (-3)2
(ii) -27 = (-3) × (-3) × (-3) = (-3)3
(iii) 81 = (-3) × (-3) × (-3) × (-3) = (-3)4

Question 10.
Find the value of x in each of the following:
(i) 7x = 343
(ii) 3x = 729
(in) (-8)x = -512
(iv) (-4)x = -1024
(v) $$\left( \frac { 2 }{ 5 } \right) ^{ x }$$ = $$\frac { 32 }{ 3125 }$$
(vi) $$\left( \frac { -3 }{ 4 } \right) ^{ x }$$ = $$\frac { -243 }{ 1024 }$$
Solution:

Question 11.
Write the prime factorization of the following numbers in the exponential form:
(i) 72
(ii) 360
(iii) 405
(iv) 540
(v) 2280
(vi) 3600
(vii) 4725
(viii) 8400
Solution:
(i) 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32

(ii) 360 = 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32 × 5

(iii) 405 = 3 × 3 × 3 × 3 × 5 = 34 × 51

(iv) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 33 × 51

(v) 2280 = 2 × 2 × 2 × 3 × 5 × 19 = 23 × 31 × 5× 191

(vi) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24 × 3× 52

(vii) 4725 = 3 × 3 × 3 × 5 × 5 × 7 = 33 × 52 × 7

(viii) 8400 = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 24 × 31 × 52 × 71