Chapter 10 — Exponents and Powers

Chapter 10 of the Class 8 Maths NCERT textbook, "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.

• Extending exponents — The chapter widens exponents to include zero and negative integers, showing that a negative exponent means a reciprocal power and that the familiar laws of exponents keep working across this larger range.
• Standard form for extremes — Very large and very small numbers are written compactly as a × 10ⁿ with a between 1 and 10, so quantities like Earth's mass or a red blood cell's diameter become easy to record and read.
• Comparing and computing — Numbers in standard form are compared and arithmetically combined by aligning them to the same power of ten, turning awkward magnitudes into manageable calculations.

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