Topic explanation
Laws of Indices is part of the Number strand in GCSE Maths. Multiply and divide powers, brackets raised to powers, and zero index rules.
Exam papers from AQA, Edexcel, OCR assess fluency (short questions) and reasoning (multi-mark). Practise reading command words (“show that”, “hence”, “give your answer in the form…”) before you rearrange algebra or interpret a result.
Key formulas & rules
- Laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ
- Standard form: N = a × 10ᵏ where 1 ≤ a < 10
- Fractions: multiply numerators/denominators; divide by flipping the second fraction
Common mistakes
- Arithmetic and sign errors when simplifying expressions involving laws of indices.
- Not answering in the required form (fraction vs decimal, surd vs rounded).
- Missing a final sentence that interprets the result in context when the question is applied.
Exam tips
- Underline key words in the question: “exact”, “integer”, “give reasons”.
- Estimate or use inverse operations to sanity-check answers when a calculator is allowed.
- Use StudyVector practice filtered to “Indices & Standard Form” to drill exam-style questions on this skill.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
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