NCERT Solutions Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2

NCERT Solutions Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 focuses on applying the laws of exponents to solve problems. In this exercise, students learn how to simplify expressions involving powers with the same base and how to use the zero exponent rule. It also explains how to handle negative exponents in a simple and clear way.

These NCERT Solutions follow the official NCERT textbook and are explained step by step to help students understand each rule easily. The solutions include simple examples and clear methods, making it easier for students to solve problems confidently. Practicing NCERT Solutions from Exercise 10.2 helps build a strong foundation in handling exponents and prepares students for more advanced calculations in higher classes.

1.0Download NCERT Solutions Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 PDF with simple, step-by-step solutions to help you learn and practice easily.

2.0Key Concepts in Exercise 10.2 of Class 8 Maths Chapter 10

Exercise 10.2 of Chapter 10 – Exponents and Powers builds on the concepts introduced in the previous exercise and focuses on applying the laws of exponents, including dealing with negative exponents. This exercise equips students with tools to simplify and calculate powers efficiently.

• Laws of Exponents in Detail
  This exercise helps students apply and master all key laws of exponents:
• $$\begin{gathered} a^m\times a^n=a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \\ (a^m{)}^n=a^{mn} \\ {a}^0=1\text{ (for }a\ne 0\text{)} \end{gathered}$$
• Negative Exponents
  Students are introduced to negative powers and their meanings.
  Example:
  $a^{-n}=\frac{1}{a^n}$
  This concept is critical for expressing small decimal values in compact exponential form.
• Simplifying Expressions
  Practice problems help students simplify expressions involving multiple laws and both positive and negative exponents.
• Comparison of Numbers Using Exponents
  Students learn to compare very large or very small numbers using exponential notation, which is especially helpful in scientific and technical contexts.
• Use of Standard Form (Scientific Notation)
  Although not deeply covered here, the base idea is introduced as a foundation for writing numbers like .

3.0NCERT Class 8 Maths Chapter 10: Other Exercises

4.0NCERT Class 8 Maths Chapter 10 Exercise 10.2: Detailed Solutions

1. Express the following numbers in standard form (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000 Sol. (i) $0.0000000000085=\frac{85}{10000000000000}$ $$\begin{gathered} =\frac{85}{10^{13}}=\frac{8.5\times 10}{10^{13}}=8.5\times 10\times 10^{-13} \\ =8.5\times 10^{-12} \end{gathered}$$ (ii) 0.00000000000942 $=\frac{942}{100000000000000}$ $=\frac{942}{10^{14}}=\frac{9.42\times 100}{10^{14}}=9.42\times 10^2\times 10^{-14}$ $=9.42\times 10^{-12}$ (iii) 6020000000000000 $=6.02\times 10^{15}$ (iv) $0.00000000837=\frac{837}{100000000000}$ $=\frac{837}{10^{11}}=\frac{8.37}{10^9}=8.37\times 10^{-9}$ (v) 31860000000 $=3.186\times 10^{10}$
2. Express the following numbers in usual form. (i) $3.02\times 10^{-6}$ (ii) $4.5\times 10^4$ (iii) $3\times 10^{-8}$ (iv) $1.0001\times 10^9$ (v) $5.8\times 10^{12}$ (vi) $3.61492\times 10^6$ Sol. (i) $3.02\times 10^{-6}=\frac{302}{100}\times \frac{1}{10^6}=\frac{302}{100000000}$ $=0.00000302$ (ii) $4.5\times 10^4=\frac{45}{10}\times 10^4=45\times 10^3=45000$ (iii) $3\times 10^{-8}=\frac{3}{10^8}=\frac{3}{100000000}$ $=0.00000003$ (iv) $1.0001\times 10^9$ $\frac{10001}{10000}\times 10^9=\frac{10001}{10^4}\times 10^9$ $=10001\times 10^{9-4}$ $=10001\times 10^5$ $=1000100000$ (ii) Charge of an electron is 0.00000000000000000016 coulomb. (iii) Size of a bacteria is 0.0000005 m . (iv) Size of a plant cell is 0.00001275 m . (v) Thickness of a thick paper is 0.07 mm . Sol. (i) 1 micron $=\frac{1}{1000000}\mathrm{m}=1\times 10^{-6}\mathrm{m}$ (ii) Charge of an electron is $=0.00000000000000000016$ $=\frac{16}{100000000000000000000}$ $=\frac{16}{10^{20}}=\frac{1.6\times 10}{10^{20}}=\frac{1.6}{10^{19}}$ $=1.6\times 10^{-19}$ coulomb (iii) Size of a bacteria $=0.0000005\mathrm{m}$ $=\frac{5}{10000000}\mathrm{m}=\frac{5}{10^7}\mathrm{m}=5\times 10^{-7}\mathrm{m}$ (iv) Size of plant cell $=0.00001275\mathrm{m}$. $=\frac{1275}{100000000}=\frac{1.275}{10^8}\times 10^3$ $=1.275\times 10^{3-8}$ $=1.275\times 10^{-5}\mathrm{m}$ (v) Thickness of a thick paper $=0.07\mathrm{mm}$. $=\frac{7}{100}=\frac{7}{10^2}=7\times 10^{-2}\mathrm{mm}$
3. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm . What is the total thickness of the stack? Sol. Thickness of one book $=20\mathrm{mm}$ $\therefore$ Thickness of 5 books $=5\times 20\mathrm{mm}=100\mathrm{mm}$ Thickness of 1 paper sheet $=0.016\mathrm{mm}$ Thickness of 5 paper sheets $=5\times 0.016\mathrm{mm}$ $=0.08\mathrm{mm}$ Total thickness $=100\mathrm{mm}+0.08\mathrm{mm}$ $=100.08\mathrm{mm}$ $=1.0008\times 10^2\mathrm{mm}$

5.0Key Features and Benefits of Class 8 Maths Chapter 10 Exercise 10.2

• Understanding Negative Exponents: Exercise 10.2 introduces the concept of negative exponents and teaches how they are used in mathematical expressions.
• Easy Application of Rules: Students learn how to apply the laws of exponents even when the powers are negative, using simple and clear steps.
• Real-Life Relevance: These concepts help in solving scientific notations and problems involving very small or large numbers, which are useful in science too.
• Strengthens Concept Clarity: This exercise improves understanding of exponent rules, boosting confidence in solving different types of exponent-based problems.
• Aligned with NCERT Textbook: All questions follow the official NCERT syllabus, making it ideal for exam preparation and school revision.