Lesson 1 of 4 · Grade 9 Mathematics
Indices and standard form
15 min
Laws of indices
- Multiplication: aᵐ x aⁿ = aᵐ⁺ⁿ. 2³ x 2⁴ = 2⁷ = 128
- Division: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. 5⁶ ÷ 5⁴ = 5² = 25
- Power of a power: (aᵐ)ⁿ = aᵐⁿ. (3²)³ = 3⁶
- Zero index: a⁰ = 1. 7⁰ = 1
- Negative index: a⁻ⁿ = 1/aⁿ. 2⁻³ = 1/8
Standard form
A number written as A x 10ⁿ where 1 ≤ A < 10.
- 45,000 = 4.5 x 10⁴
- 0.0036 = 3.6 x 10⁻³
- The distance from the Earth to the Sun is about 150,000,000 km = 1.5 x 10⁸ km.
Key points to remember
- Multiply: add the powers
- Divide: subtract the powers
- a⁰ = 1; a⁻ⁿ = 1/aⁿ
- Standard form: A x 10ⁿ with 1 ≤ A < 10
Test yourself
