## 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} × 5^{2}

(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

= 2^{6} × 3^{1} × 5^{3}

(ii) 12600

= 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7

= 2^{3} × 3^{2} × 5^{2} × 7^{1}

(iii) 14157

= 3 × 3 × 11 × 11 × 13

= 3^{2} × 11^{2} × 13^{1}

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 × 10^{9} cubic km

(ii) The population of India was about 1,027,000,000 in march, 2001.

= 1.027 × 10^{9}

(iii) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water.

6.023 × 10^{22} molecules

Question 7.

Compare the following numbers:

(i) 5.976 × 10^{24}; 8.689 × 10^{23}

(ii) 3.7662 × 10^{17}; 3.7671 × 10^{17}

Solution:

(i) 5.976 × 10^{24}; 8.689 × 10^{23}

Here in 5.976 × 10^{24}, 10^{2} is greater then in 8.689 × 10^{23}

5.976 × 10^{24} > 8.689 × 10^{23}

(ii) 3.7662 × 10^{17}; 3.7671 × 10^{17}

Here 10^{17} is multiplied in both

and 76671 > 7662

3.76671 × 10^{17} > 3.7662 × 10^{17}