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ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Check Your Progress

Question 1.
Find the value of each of the following:
(i) (-3)³ × 5²
(ii) (-1)⁵⁰¹ × [(27)⁴ ÷ (9)⁵]
(iii) \(\left( -3\frac { 1 }{ 2 } \right) ^{ 3 }\)
Solution:

Question 2.
Simplify the following:

Solution:

Question 3.
Simplify and write the following in exponential form:

Solution:

Question 4.

Solution:

Question 5.
Write the prime factorisation of the following numbers in the exponential form:
(i) 24000
(ii) 12600
(iii) 14157
Solution:

Question 6.
Express the numbers appearing in the following statements in scientific notation:
(i) The earth has 1,353,000,000 cubic km of water.
(ii) The population of India was about 1,027,000,000 in march, 2001.
(iii) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water.
Solution:

Question 7.
Compare the following numbers:
(i) 5.976 × 10²⁴; 8.689 × 10²³
(ii) 3.7662 × 10¹⁷; 3.7671 × 10¹⁷
Solution:

ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) In the expression (-5)⁹, exponent = ……… and base = ………..
(ii) If the base is \(\frac { -3 }{ 4 }\) and exponent is 5, then exponential form is ………
(iii) The expression (x²y⁵)³ in the simplest form is ………
(iv) If (100)⁰ = 10ⁿ, then the value of n is ……..

(ix) 35070000 = 3.507 × 10^….
(x) If (-2)ⁿ = -128, then n = ……..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) If a is a rational number then a^m × aⁿ = a^m×n
(ii) 2³ × 3² = 6⁵.
(iii) The value of (-2)^-3 is \(\frac { -1 }{ 8 }\).
(iv) The value of the expression 2⁹ × 2⁹¹ – 2¹⁹ × 2⁸¹ is 1.
(v) 3⁰ = (1000)⁰.
(vi) 5⁶ ÷ (-2)⁶ = \(\frac { -5 }{ 2 }\)
(vii) 5⁰ × 3⁰ = 8⁰
(viii) \(\frac { { 2 }^{ 3 } }{ 7 } <\left( \frac { 2 }{ 7 } \right) ^{ 3 }\)
(ix) (10 + 10)⁴ = 10⁴ + 10⁴.
(x) x⁰ × x⁰ = x⁰ ÷ x⁰, where x is a non-zero rational number.
(xi) 4⁹ is greater than 16³.
(xii) x^m + x^m = x^2m, where x is a non-zero rational number and m is a positive integer.
(xiii) \(\left( \frac { 4 }{ 3 } \right) ^{ 5 }\times \left( \frac { 5 }{ 7 } \right) ^{ 5 }=\left( \frac { 4 }{ 3 } +\frac { 5 }{ 7 } \right) ^{ 5 }\)
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 18):
Question 3.
a × a × a × b × b × b is equal to
(a) a³b²
(b) a²b³
(c) (ab)³
(d) a⁶b6
Solution:

Question 4.
(-2)³ × (-3)² is equal to
(a) 6⁵
(b) (-6)⁶
(c) 72
(d) -72
Solution:

Question 5.
The expression (pqr)³ is equal to
(a) p³qr
(b) pq³r
(c) pqr³
(d) p³q³r³
Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.
The value of (5³⁰ × 5²⁰) ÷ (5⁵)⁹ in the exponential form is
(a) 5^-5
(b) 5⁵
(c) 5⁵⁰
(d) 5⁹⁵
Solution:

Question 9.
The law \(\left( \frac { a }{ b } \right) ^{ n }=\frac { { a }^{ n } }{ b^{ n } }\) does not hold when
(a) a = 3, b = 2
(b) a = -2, b = 3
(c) n = 0
(d) b = 0
Solution:

Question 10z

Solution:

Question 11.

Solution:

Question 12.
The value of 5^-1 – 6^-1 is
(a) \(\frac { 1 }{ 30 }\)
(b) \(\frac { -1 }{ 30 }\)
(c) 30
(d) -30
Solution:

Question 13.
The value of (6^-1 – 8^-1)^-1 is
(a) \(\frac { -1 }{ 2 }\)
(b) -2
(c) \(\frac { 1 }{ 24 }\)
(d) 24
Solution:

Question 14.

Solution:

Question 15.
If 2³ + 1³ = 3^x, then the value of x is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:

Question 16.
The standard form of 751.65 is
(a) 7.5165 × 10²
(b) 75.165 × 10¹
(c) 7.5165 × 10⁴
(d) 7.51 × 10²
Solution:

Question 17.
The usual form of 5.658 × 10⁵ is
(a) 5658
(b) 56580
(c) 565800
(d) 5658000
Solution:

Question 18.
Which of the following numbers is in the standard form?
(a) 26.57 × 10⁴
(b) 2.657 × 10⁴
(c) 265.7 × 10³
(d) 0.2657 × 10⁶
Solution:

Value Based Questions

Question 1.
Typhoid is caused by bacteria Salmonella typhi. The size of Salmonella typhi is about 0.0000000005 mm. Express it in standard form. Vinay is suffering from typhoid, his doctor advised him to take healthy food and avoid eating food or drinking beverages from street vendors.
Why should we eat healthy food and why should we not eat food from street vendors?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.

Solution:

Question 2.

Solution:

ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Ex 4.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Ex 4.3

Question 1.
Write the following numbers in the standard form (or scientific notation):
(i) 530.7
(ii) 3908.78
(iii) 39087.8
(iv) 2.35
(v) 3,43,000
(vi) 70,00,000
(vii) 3,18,65,00,000
(viii) 893,000,000
(ix) 70,040,000,000
Solution:

Question 2.
Write the following numbers in usual decimal notation:
(i) 4.7 × 10³
(ii) 1.205 × 10⁵
(iii) 1.234 × 10⁶
(iv) 4.87 × 10⁷
(v) 6.05 × 10⁸
(vi) 9.083 × 10¹¹
Solution:

Question 3.
Express the numbers appearing in the following statements in scientific notation (or standard form):
(i) The distance between the earth and the moon is 384,000,000 m.
(ii) The diameter of the sun is 1,400,000,000m.
(iii) The universe is estimated to be about 12,0000,000 years old.
(iv) In a galaxy, there are on an average 100,000,000,000 stars.
(v) The distance of the sun from the centre of milky way galaxy is estimated to be 300,000,000,000,000,000 km.
(vi) The astronomical distance of unit is a light year (a light year is a distance travelled by the light in one year). A light year is about 9,467,500,000,000 kilometers.
Solution:

Question 4.
Compare the following numbers:
(i) 4.3 × 10¹⁴; 3.01 × 10¹⁷
(ii) 1.439 × 10¹²; 1.4335 × 10¹²
Solution:

Question 5.
Write the following numbers in the expanded Exponential form:
(i) 279404
(ii) 3006194
(iii) 28061906
Solution:

Question 6.
Find the number from each of the expanded form:
(i) 3 × 10⁴ + 7 × 10² + 5 × 10⁰
(ii) 4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰
(iii) 8 × 10⁷ + 3 × 10⁴ + 7 × 10³ + 5 × 10² + 8 × 10¹
Solution:

ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Ex 4.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 4 Exponents and Powers Ex 4.2

Question 1.
Using laws of exponents, simplify and write the following in the exponential form:

Solution:

Question 2.
Simplify and write the following in the exponential form:
(i) 5³ × 5⁷ × 5¹²
(ii) a⁵ × a³ × a⁷
(iii) (7¹² × 7³) ÷ 7⁴
Solution:

Question 3.
Simplify and write the following in the exponential form:
(i) (2²)¹⁰⁰
(ii) ((-7)⁶)⁵
(iii) (3²)⁵ × (3⁴)⁷
Solution:

Question 4.
Simplify and write in the exponential form:

Solution:

Question 5.
Simplify and write in the exponential form:

Solution:

Question 6.
Simplify and express each of the following in the exponential form:

Solution:

Question 7.
Express each of the following rational numbers in the exponential form:

Solution:

Question 8.
Simplify the following:

Solution:

Question 9.
Simplify the following:

Solution:

Question 10.
Simplify the following:

Solution:

Question 11.
Simplify:

Solution:

Question 12.
Express each of the following as a product of prime factors in the exponential form:
(i) 108 × 192
(ii) 729 × 64
(iii) 384 × 147
Solution:

Question 13.
Simplify and write the following in the exponential form:
(i) 3³ × 2² + 2² × 5⁰
(ii) 9² + 11² – 2² × 3 × 17⁰
Solution:

Question 14.
(i) By what number should we multiply 3⁴ so that the product is 3⁷?
(ii) By what number should be multiple (-6)^-1 so that the product is 10^-1?
Solution:

Question 15.

Solution:

ML Aggarwal Class 7 Solutions Chapter 4 Exponents and Powers Ex 4.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

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:

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:

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:

Question 4.
Simplify the following:
(i) 7 × 10³
(ii) ²⁵ × 9
(iii) 3³ × 10⁴
Solution:

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:

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:

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

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

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

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: