Powers & Roots

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

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-2
  • NA6-2
New NZC (2026)
  • NZC26-P4-NUM-NSO-P-Y9-05
  • NZC26-P4-NUM-NSO-P-Y9-06
  • NZC26-P4-NUM-NSO-P-Y10-03
  • NZC26-P4-ALG-ER-K-Y10-03
  • NZC26-P4-NUM-NSO-K-Y10-02
  • NZC26-P4-NUM-NSO-K-Y10-03
  • NZC26-P4-ALG-ER-K-Y10-02
  • NZC26-P4-NUM-NSO-K-Y10-04
  • NZC26-P4-NUM-NSO-P-Y10-08
  • NZC26-P4-NUM-NSO-K-Y9-02
  • NZC26-P4-NUM-NSO-P-Y10-04
  • NZC26-P3-NUM-NSO-K-Y7-02
  • NZC26-P3-NUM-NSO-K-Y7-03
  • NZC26-P3-NUM-NSO-K-Y8-02
  • NZC26-P3-NUM-NSO-P-Y7-03
  • NZC26-P3-NUM-NSO-P-Y7-04
  • NZC26-P3-NUM-NSO-P-Y8-04
  • NZC26-P3-NUM-NSO-P-Y8-05
  • NZC26-P3-NUM-NSO-P-Y8-06

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.

Where this fits

What leads into this objective, and where it goes next.

Before

No prerequisite objective linked yet.

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Powers & Roots

Powers & Roots

Do

Identifying powers of 2 through to 2^10

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-P-Y9-05
Do

Converting between negative powers and unit fractions (e.g. 3^−2 = 1/9)

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-P-Y9-06

Next

Irrational numbers

Irrational numbers

Surds -- simplifying, multiplying, dividing, and adding/subtracting

Surds -- simplifying, multiplying, dividing, and adding/subtracting

Also under NA5-2:

Also under NA6-2:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.