Multiplying Expressions (with powers)

Simplify products with the same base by adding exponents, apply the rule in algebra and area contexts, and explain what stays out of scope.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-6
New NZC (2026)
  • NZC26-P4-NUM-NSO-P-Y9-10

Resources

  • Alpha textbook: Just letters, Ex 13.04, pg 209
  • Alpha textbook: Numbers and letters, Ex 13.05, pg 210
  • Alpha textbook: Multiplying with indices, Ex 13.08, pg 214
  • CorbettMaths Laws of IndicesQuestions PDF · Answers

Terminology

  • variable
  • coefficient
  • exponent
  • power
  • index
  • base
  • product
  • simplify
  • area

Task goals

  • Use the product law for the same base, for example $a^3\times a^4=a^7$ and $2^3\times2^2=2^5$.
  • Multiply coefficients separately and then add exponents for matching variables, such as $4a^2\times3a^5=12a^7$.
  • Keep different variables separate while simplifying products such as $2x^3y\times5x^2y^4=10x^5y^5$.
  • Form and simplify area expressions such as a square with side $3y^4$ or a rectangle with sides $4x^2y$ and $3xy^4$.

Where this fits

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

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Multiplying Expressions (with powers)

Multiplying Expressions (with powers)

Do

Generalising about exponents of 0 and 1

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-P-Y9-10

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