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0580/22 Oct/Nov 2021, Question 13: Laws of Indices

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Express 243 times 27 to the power 2n as one power of 3, then express 6k² as a prime-factor product when k = 2 × 3² × p³ with p a prime above 3.

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Part (a) · 2 marks

Combine 243 and 27²ⁿ into a single power of 3, giving the exponent in terms of n.

  1. 1243 = 3⁵ and 27²ⁿ = (3³)²ⁿ = 3⁶ⁿ
  2. 2243 × 27²ⁿ = 3⁵ × 3⁶ⁿ = 3⁶ⁿ⁺⁵

Answer3⁶ⁿ⁺⁵

Part (b) · 2 marks

Using k = 2 × 3² × p³, give 6k² as a product of primes involving p.

  1. 1k² = 2² × 3⁴ × p⁶
  2. 26k² = 2 × 3 × 2² × 3⁴ × p⁶
  3. 36k² = 2³ × 3⁵ × p⁶

Answer2³ × 3⁵ × p⁶

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Also searched as: 0580/22/O/N/21 · 0580_w21_qp_22 · 0580 w21 22 · question 13.
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