## 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 × 10^{13}

Question 12.

Express the following numbers in the usual form:

(i) 5.73 × 10^{-11}

(ii) 3.895 × 10^{15}.

Solution:

(i) 5.73 × 10^{-11 }= 0.0000000000573

(ii) 3.895 × 10^{15 }= 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 × 10^{24} kg and mass of the Moon is 7.35 × 10^{22} kg. What is the difference of their masses?

Solution:

Mass of Earth = 5.97 × 10^{24} kg

and mass of Moon = 7.35 × 10^{22} kg

∴ Difference = (5.97 × 10^{24}) – (7.35 × 10^{22})

= 10^{22} (5.97 × 10^{2} – 7.35)

= 10^{22} (597 – 7.35) = 589.65 × 10^{22}

= 5.8965 × 10^{2} × 10^{22}

= 5.8965 × 10^{24}