Chapter 10 — Exponents and Powers

Chapter 10 of Class 8 maths, "Exponents and Powers", teaches how to work with exponents including negative exponents, and how to express very large and very small numbers in standard form using powers of 10.

This chapter extends the concept of exponents to include negative and zero exponents. Students learn the laws of exponents (product rule, quotient rule, power rule, and more) that apply even when exponents are negative integers. The chapter then focuses on expressing very large numbers (like the mass of Earth: 5.97 × 10²⁴ kg) and very small numbers (like the diameter of a red blood cell: 7 × 10⁻⁶ m) in standard form. Students also learn to compare numbers expressed in standard form and perform arithmetic operations on them.

1. 01Negative exponents: for any non-zero integer a, a⁻ᵐ = 1/aᵐ, where m is a positive integer
2. 02Laws of exponents extend to negative and zero exponents: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1
3. 03Standard form: expressing numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer (positive for large numbers, negative for small numbers)
4. 04Very large numbers example: Earth-Sun distance is 1.496 × 10¹¹ m; very small numbers example: red blood cell diameter is 7 × 10⁻⁶ m
5. 05Comparing and performing arithmetic on numbers in standard form by converting to the same power of 10