## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Check Your Progress

Question 1.
Evaluate: Solution: Question 2.
Simplify:  Solution:  Question 3.
Find the multiplicative inverse of $$\left(\frac{125}{27}\right)^{\frac{-2}{3}}$$
Solution: ∴ Multiplicative inverse $$\frac{9}{25}=\frac{25}{9}$$

Question 4.
Simplify and write in exponential form: Solution:  Question 5.
Simplify: $$\frac{5^{n+2}-6+5^{n+1}}{13 \times 5^{n}-2 \times 5^{n+1}}$$
Solution: Question 6.
Prove that (a + b)-1 (a-1 + b-1) = (ab)-1.
Solution:
(a + b)-1 (a-1 + b-1) = (ab)-1
L.H.S. = (a + b)-1 (a-1 + b-1)  Hence, Proved L.H.S. = R.H.S.

Question 7.
Find the value of x for which Solution: Question 8.
If $$\frac{2^{-n} \times 8^{2 n+1} \times 16^{2 n}}{4^{3 n}}=\frac{1}{16}$$, find the value of n.
Solution:  Question 9.
By what number should $$\left[\left(\frac{-5}{2}\right)^{3}\right]^{-3}$$ be multiplied to get $$\left(\frac{-2}{5}\right)^{5}$$?
Solution:  Question 10.
By what number should $$\left(\frac{-3}{2}\right)^{-4}$$ be divided to get $$\left(\frac{-2}{3}\right)^{3}$$?
Solution: Question 11.
Express the following numbers in standard form:
(i) 0.0000000003904
(ii) 12730000000000
Solution:
(i) 0.0000000003904 = 3.904 × 10-10
(ii) 12730000000000 = 1.273 × 1013

Question 12.
Express the following numbers in the usual form:
(i) 5.73 × 10-11
(ii) 3.895 × 1015.
Solution:
(i) 5.73 × 10-11 = 0.0000000000573
(ii) 3.895 × 1015 = 3895000000000000

Question 13.
If $$\left(\frac{9}{4}\right)^{-4} \times\left(\frac{2}{3}\right)^{3}=\left(\frac{p}{q}\right)^{11}$$, then find the value of $$\left(\frac{p}{q}\right)^{-2}$$.
Solution:  Question 14.
Mass of the Earth is 5.97 × 1024 kg and mass of the Moon is 7.35 × 1022 kg. What is the difference of their masses?
Solution:
Mass of Earth = 5.97 × 1024 kg
and mass of Moon = 7.35 × 1022 kg
∴ Difference = (5.97 × 1024) – (7.35 × 1022)
= 1022 (5.97 × 102 – 7.35)
= 1022 (597 – 7.35) = 589.65 × 1022
= 5.8965 × 102 × 1022
= 5.8965 × 1024