Class 8 Maths – Chapter 12
Exponents & Powers
STEP 4: Quick Revision Notes

1. What is an Exponent?
An exponent shows how many times a number is multiplied by itself.

Example:
2³ = 2 × 2 × 2 = 8
Here, 2 is the base and 3 is the exponent.

2. Laws of Exponents (Very Important)

(a) Same base – Add powers
aᵐ × aⁿ = aᵐ⁺ⁿ
Example: 2² × 2³ = 2⁵

(b) Same base – Subtract powers
aᵐ ÷ aⁿ = aᵐ⁻ⁿ (m > n)
Example: 5⁴ ÷ 5² = 5²

(c) Power of a power
(aᵐ)ⁿ = aᵐⁿ
Example: (2³)² = 2⁶

(d) Power of a product
(ab)ⁿ = aⁿbⁿ
Example: (2×3)² = 2² × 3²

3. Zero Exponent
Any non-zero number raised to power 0 is equal to 1.

a⁰ = 1
Example: 7⁰ = 1

4. Negative Exponent
a⁻ⁿ = 1 / aⁿ

Example:
2⁻³ = 1 / 2³ = 1 / 8

5. Powers of 10
10¹ = 10
10² = 100
10³ = 1000

Used to write very large numbers easily.

⭐ Exam Tip for Students:
• Learn laws clearly
• Write steps neatly
• One law = one mark