Topic explanation
Understand and use the laws of indices for all rational exponents and manipulate surds.
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 surds.
- 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 “Surds” 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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