Indices & Standard Form
Powers are a shortcut for repeated multiplication — and for writing huge or tiny numbers.
Laws of indicesZero & negative powersStandard formCalculating in standard form
📖 Learn
Multiply → add
a³ × a⁴ = a⁷. Divide → subtract: a⁶ ÷ a² = a⁴. Power of a power → multiply: (a²)³ = a⁶.
Zero & negative
a⁰ = 1. a⁻² = 1/a². So 2⁻³ = 1/8.
Standard form
A × 10ⁿ with 1 ≤ A < 10. 45,000 = 4.5 × 10⁴; 0.003 = 3 × 10⁻³.
Worked example
Write 6,200,000 in standard form
- 1Put the point after the first digit: 6.2
- 2The point moved 6 places.
- 36.2 × 10⁶ ✅
⭐ Practise
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