Indices, Powers and Roots
Use index laws, integer and fractional powers, roots and exact relationships.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Integer index laws
Exam cue: Express terms with the same base, apply one index law at a time and distinguish multiplication from addition.
Concept 2
Powers and roots
Exam cue: Substitute a simple positive value or reverse the power with a root to test the result.
Concept 3
Zero, negative and fractional indices
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Foundation uses squares, cubes, roots and integer index laws in accessible forms. Higher extends to zero, negative and fractional indices and more demanding algebraic use.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Adding indices when terms are added rather than multiplied.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Multiply same base
Add the indices.
Divide same base
Subtract the indices.
Fractional index
The denominator gives the root and the numerator gives the power.
Indices, Powers and Roots: method
Express terms with the same base, apply one index law at a time and distinguish multiplication from addition.
Indices, Powers and Roots: check
Substitute a simple positive value or reverse the power with a root to test the result.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Evaluate 2⁵×2³.
Foundation · AO1 technique · Non-calculator — Evaluate 5⁷÷5⁴.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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