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Powers & Scientific Notation — Making Big & Small Numbers Easy - Leejohnston - 11-13-2025
Powers & Scientific Notation — Making Big & Small Numbers Easy
Powers (also called indices or exponents) are a quick way to write repeated multiplication.
Scientific notation is a clean way to write very big or very small numbers.
These are essential skills for GCSE maths and all sciences.
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1. What Are Powers?
A power tells you how many times to multiply a number by itself.
Examples:
• 3² = 3 × 3 = 9
• 5³ = 5 × 5 × 5 = 125
• 10⁴ = 10,000
Terminology:
3² → 3 is the base, 2 is the index (or exponent).
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2. Key Power Rules
Rule 1: Add powers when multiplying same bases
aᵐ × aⁿ = aᵐ⁺ⁿ
Example:
2³ × 2² = 2⁵ = 32
Rule 2: Subtract powers when dividing
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Example:
10⁶ ÷ 10² = 10⁴
Rule 3: Power of a power
(aᵐ)ⁿ = aᵐⁿ
Example:
(3²)³ = 3⁶ = 729
Rule 4: Negative powers
a⁻ⁿ = 1 / aⁿ
Example:
10⁻³ = 1/1000 = 0.001
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3. What Is Scientific Notation?
Scientific notation writes numbers as:
(number between 1 and 10) × 10^(power)
Examples:
• 4,200 = 4.2 × 10³
• 0.005 = 5 × 10⁻³
• 73,000 = 7.3 × 10⁴
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4. Converting to Scientific Notation
Move the decimal point until you get a number between 1 and 10.
If you move left → positive power
Example:
52,000 → 5.2 × 10⁴
If you move right → negative power
Example:
0.0037 → 3.7 × 10⁻³
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5. Multiplying & Dividing in Scientific Notation
Multiply numbers, add powers
(3 × 10²) × (2 × 10³)
= 6 × 10⁵
Divide numbers, subtract powers
(9 × 10⁶) ÷ (3 × 10²)
= 3 × 10⁴
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6. Why This Matters
You’ll use powers and scientific notation in:
• GCSE Maths
• GCSE Science
• Chemistry (moles, atoms, small quantities)
• Physics (distances, speeds, forces)
• Computing & algorithms
• Astronomy (huge distances)
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Summary
Powers simplify repeated multiplication.
Scientific notation simplifies very big or very small numbers.
Once you master these:
• Calculations become faster
• GCSE questions become easier
• Scientific data becomes clearer
This skill is essential for higher-level work in maths and science.