Powers & Roots

Interpret, evaluate, compare, and apply positive, zero, and negative powers together with square and cube roots.

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Te reo Māori terms

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Related resources in Measurement

Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Alpha textbook: Powers & Roots (Check Your Understanding on pgs 92 & 93)
  • Alpha textbook: Covers basic powers (squares, cubes, and square roots only)
  • Dr Austin Maths - Algebraic Laws of Indices Practice GridQuestions PDF · Answers
  • Dr Austin Maths - Powers and Roots Revision Practice GridQuestions PDF · Answers
  • CorbettMaths Negative Indices (Foundation GCSE)Questions PDF · Answers
  • Beta: Skills in Ex 1.11, pg 23

Terminology

  • power
  • exponent
  • index
  • base
  • squared
  • cubed
  • square root
  • cube root
  • reciprocal

Task goals

  • Rewrite repeated multiplication as powers and evaluate positive, zero, and negative exponents.
  • Connect square and cube roots to area, volume, and the inverse of powers.
  • Compare powers carefully, including signs, brackets, and reciprocal forms.
  • Estimate non-perfect roots by bounding them between nearby perfect squares or cubes.

Key skills

  • Powers
  • Roots
  • Square root
  • Cube root
  • Indices

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included
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For teachers

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