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

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

ML Aggarwal Class 8 Solutions for ICSE Maths