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

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:
(i) 24000

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5
= 2⁶ × 3¹ × 5³
(ii) 12600

= 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7
= 2³ × 3² × 5² × 7¹
(iii) 14157

= 3 × 3 × 11 × 11 × 13
= 3² × 11² × 13¹

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:
(i) The earth has 1,353,000,000 cubic km of water.
= 1.353 × 10⁹ cubic km
(ii) The population of India was about 1,027,000,000 in march, 2001.
= 1.027 × 10⁹
(iii) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water.
6.023 × 10²² molecules

Question 7.
Compare the following numbers:
(i) 5.976 × 10²⁴; 8.689 × 10²³
(ii) 3.7662 × 10¹⁷; 3.7671 × 10¹⁷
Solution:
(i) 5.976 × 10²⁴; 8.689 × 10²³
Here in 5.976 × 10²⁴, 10² is greater then in 8.689 × 10²³
5.976 × 10²⁴ > 8.689 × 10²³
(ii) 3.7662 × 10¹⁷; 3.7671 × 10¹⁷
Here 10¹⁷ is multiplied in both
and 76671 > 7662
3.76671 × 10¹⁷ > 3.7662 × 10¹⁷

ML Aggarwal Class 7 Solutions for ICSE Maths