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4MA1/1HR Jun 2022, Question 12: Laws of Indices

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks

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The question, in short

Given P = 3³ × 5² × 7 and Q = 3² × 5 × 7², find the HCF of P and Q, then express P³ × Q in the form 3ˣ × 5ʸ × 7ᶻ.

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Part (a) · 1 mark

Write down the highest common factor of P and Q.

  1. 1Take the lowest power of each common prime factor.
  2. 2For 3: min(3, 2) = 2 → 3²
  3. 3For 5: min(2, 1) = 1 → 5¹
  4. 4For 7: min(1, 2) = 1 → 7¹
  5. 5HCF = 3² × 5 × 7

Answer3² × 5 × 7

Part (b) · 2 marks

Work out P³ × Q and give the answer as 3ˣ × 5ʸ × 7ᶻ with positive integer x, y, z.

  1. 1P = 3³ × 5² × 7
  2. 2Q = 3² × 5 × 7²
  3. 3P³ = (3³)³ × (5²)³ × (7)³ = 3⁹ × 5⁶ × 7³
  4. 4P³ × Q = (3⁹ × 5⁶ × 7³) × (3² × 5 × 7²)
  5. 5Add exponents: 3^(9+2) × 5^(6+1) × 7^(3+2)
  6. 63¹¹ × 5⁷ × 7⁵

Answer3¹¹ × 5⁷ × 7⁵

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