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

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:
(i) 5³ × 5⁷ × 5¹² = 5³⁺⁷⁺¹² = 5²²
{∵ a^m × aⁿ × a^p = a^m+n+p}
(ii) a⁵ × a³ × a⁷ = a⁵⁺³⁺⁷ = a¹⁵
(iii) (7¹²× 7³) ÷ 7⁴ = 7¹²⁺³ ÷ 7⁴ = 7¹⁵ – 7⁴ = 7^15-4 = 7¹¹

Question 3.
Simplify and write the following in the exponential form:
(i) (2²)¹⁰⁰
(ii) ((-7)⁶)⁵
(iii) (3²)⁵ × (3⁴)⁷
Solution:
Using (a^m)ⁿ = a^mn
(i) (2²)¹⁰⁰ = 2^2×100 = 2²⁰⁰ {(a^m)ⁿ = a^mn}
(ii) [(-7)⁶]⁵ = (-7)^6×5 = (-7)³⁰
(iii) (3²)⁵ × (3⁴)⁷ = 3^2×5 × 3^4×7 = 3¹⁰ × 3²⁸ = 3¹⁰⁺²⁸ = 3³⁸

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:
(i) Product = 3⁷
Required number = 3⁷ ÷ 3⁴ = 3^7-4 = 3³ = 27
(ii) Product = 10^-1
Required number = 10^-1 ÷ (-6)^-1

Question 15.

Solution:

ML Aggarwal Class 7 Solutions for ICSE Maths