NCERT Class 8 Mathematics Mathematics: Chapter 10 — Exponents and Powers
This chapter, 'Exponents and Powers,' from NCERT Class 8 Mathematics, introduces students to the concept of using exponents to represent large numbers conveniently. It revisits the definition of exponents and explores powers with negative exponents. The chapter explains how a negative exponent like a⁻ᵐ is the multiplicative inverse of aᵐ. It demonstrates this with examples using base 10 and base 3, showing the pattern as exponents decrease. Students learn to express numbers in expanded form using positive and negative exponents, such as 1425.36 = 1 × 10³ + 4 × 10² + 2 × 10¹ + 5 × 10⁰ + 3 × 10⁻¹ + 6 × 10⁻². The chapter includes 'Try These' sections to reinforce understanding of multiplicative inverses and number expansion.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 10 — Exponents and Powers |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 332 |
Learning outcomes
- Understand and use exponents to represent large numbers.
- Define and calculate powers with negative exponents.
- Identify the multiplicative inverse of a number with a positive exponent.
- Express numbers in expanded form using positive and negative exponents.
Vocabulary
| Word | Meaning |
|---|---|
| Exponents | A number showing how many times a base number is multiplied by itself. |
| Powers | The result of a number being raised to an exponent. |
| Negative Exponent | An exponent that is a negative integer (e.g., a⁻ᵐ). |
| Multiplicative Inverse | A number that, when multiplied by another number, results in 1. For aᵐ, it is a⁻ᵐ. |
| Base | The number that is being multiplied by itself. |
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Practice questions
- What is the value of 10⁻³? Answer: 1/1000
- Find the multiplicative inverse of 2⁻⁴. Answer: 2⁴ or 16
- Expand 1025.63 using exponents. Answer: 1 × 10³ + 0 × 10² + 2 × 10¹ + 5 × 10⁰ + 6 × 10⁻¹ + 3 × 10⁻²
Frequently asked questions
What is the meaning of 10 raised to the power 24?
It means 10 multiplied by itself 24 times, often used to represent very large numbers like the mass of the Earth.
How is a negative exponent defined?
A negative exponent, like a⁻ᵐ, is defined as the multiplicative inverse of aᵐ, meaning a⁻ᵐ = 1/aᵐ.
What is the multiplicative inverse of 3²?
The multiplicative inverse of 3² is 3⁻², which is equal to 1/3² or 1/9.
How can we write 10⁻¹?
10⁻¹ is equal to 1/10, or 0.1.
What is the expanded form of 1425.36 using exponents?
1425.36 = 1 × 10³ + 4 × 10² + 2 × 10¹ + 5 × 10⁰ + 3 × 10⁻¹ + 6 × 10⁻².
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Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 10 — Exponents and Powers. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.