What is covered in Exercise 10.2 of Class 8 Maths Chapter 10?

Exercise 10.2 deals with negative exponents and how to simplify expressions that include positive and negative powers. It also helps students learn how to express small numbers in standard form using exponents.

What are negative exponents, and how are they used?

Negative exponents represent the reciprocal of a number with a positive exponent. They are used to express very small quantities compactly.

How do NCERT Solutions help with Exercise 10.2?

NCERT Solutions provide easy-to-understand steps for each question and explain how to apply the rules of exponents, especially when negative powers and standard form are involved.

NCERT Solutions

Class 8

Maths

Chapter 10 Exponents and Powers

Exercise 10.2

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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.

NCERT Solutions Class 8 Maths Chapter 10 Exercise 10.2

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:
$a^{m} \times a^{n} = a^{m + n} \frac{a ^{m}}{a ^{n}} = a^{m - n} (a^{m})^{n} = a^{mn} a^{0} = 1 (for a \neq = 0)$
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

NCERT Solutions Class 8 Maths Chapter 10 : Exercise 10.1

NCERT Solutions Class 8 Maths Chapter 10 : Exercise 10.2

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

Express the following numbers in standard form (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000 Sol. (i) $0.0000000000085 = \frac{85}{10000000000000}$ $= \frac{85}{1 0 ^{13}} = \frac{8.5 \times 10}{1 0 ^{13}} = 8.5 \times 10 \times 1 0^{- 13} = 8.5 \times 1 0^{- 12}$ (ii) 0.00000000000942 $= \frac{942}{100000000000000}$ $= \frac{942}{1 0 ^{14}} = \frac{9.42 \times 100}{1 0 ^{14}} = 9.42 \times 1 0^{2} \times 1 0^{- 14}$ $= 9.42 \times 1 0^{- 12}$ (iii) 6020000000000000 $= 6.02 \times 1 0^{15}$ (iv) $0.00000000837 = \frac{837}{100000000000}$ $= \frac{837}{1 0 ^{11}} = \frac{8.37}{1 0 ^{9}} = 8.37 \times 1 0^{- 9}$ (v) 31860000000 $= 3.186 \times 1 0^{10}$
Express the following numbers in usual form. (i) $3.02 \times 1 0^{- 6}$ (ii) $4.5 \times 1 0^{4}$ (iii) $3 \times 1 0^{- 8}$ (iv) $1.0001 \times 1 0^{9}$ (v) $5.8 \times 1 0^{12}$ (vi) $3.61492 \times 1 0^{6}$ Sol. (i) $3.02 \times 1 0^{- 6} = \frac{302}{100} \times \frac{1}{1 0 ^{6}} = \frac{302}{100000000}$ $= 0.00000302$ (ii) $4.5 \times 1 0^{4} = \frac{45}{10} \times 1 0^{4} = 45 \times 1 0^{3} = 45000$ (iii) $3 \times 1 0^{- 8} = \frac{3}{1 0 ^{8}} = \frac{3}{100000000}$ $= 0.00000003$ (iv) $1.0001 \times 1 0^{9}$ $\frac{10001}{10000} \times 1 0^{9} = \frac{10001}{1 0 ^{4}} \times 1 0^{9}$ $= 10001 \times 1 0^{9 - 4}$ $= 10001 \times 1 0^{5}$ $= 1000100000$ (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 $= \frac{1}{1000000} m = 1 \times 1 0^{- 6} m$ (ii) Charge of an electron is $= 0.00000000000000000016$ $= \frac{16}{100000000000000000000}$ $= \frac{16}{1 0 ^{20}} = \frac{1.6 \times 10}{1 0 ^{20}} = \frac{1.6}{1 0 ^{19}}$ $= 1.6 \times 1 0^{- 19}$ coulomb (iii) Size of a bacteria $= 0.0000005 m$ $= \frac{5}{10000000} m = \frac{5}{1 0 ^{7}} m = 5 \times 1 0^{- 7} m$ (iv) Size of plant cell $= 0.00001275 m$ . $= \frac{1275}{100000000} = \frac{1.275}{1 0 ^{8}} \times 1 0^{3}$ $= 1.275 \times 1 0^{3 - 8}$ $= 1.275 \times 1 0^{- 5} m$ (v) Thickness of a thick paper $= 0.07 mm$ . $= \frac{7}{100} = \frac{7}{1 0 ^{2}} = 7 \times 1 0^{- 2} mm$
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 $= 20 mm$ $∴$ Thickness of 5 books $= 5 \times 20 mm = 100 mm$ Thickness of 1 paper sheet $= 0.016 mm$ Thickness of 5 paper sheets $= 5 \times 0.016 mm$ $= 0.08 mm$ Total thickness $= 100 mm + 0.08 mm$ $= 100.08 mm$ $= 1.0008 \times 1 0^{2} mm$

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.

NCERT Class 8 Maths Ch. 10 Exponents and Powers Other Exercises:-

Exercise 10.1

Exercise 10.2

NCERT Solutions for Class 8 Maths Other Chapters:-

Chapter 1: Rational Numbers

Chapter 2: Linear Equations in One variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Data Handling

Chapter 5: Squares and Square Roots

Chapter 6: Cubes and Cube Roots

Chapter 7: Comparing Quantities

Chapter 8: Algebraic Expressions and Identities

Chapter 9: Mensuration

Chapter 10: Exponents and Powers

Chapter 11: Direct and Inverse Proportions

Chapter 12: Factorisation

Chapter 13: Introduction of Graphs