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

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) 7^x = 343
(ii) 3^x = 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 × 5¹ × 19¹

(vi) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2⁴ × 3² × 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

ML Aggarwal Class 7 Solutions for ICSE Maths