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4MA1/1H Jan 2023, Question 12: Laws of Indices

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 2 marks

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The question, in short

Two index equations: find m from 3^(1/2) × 3^(2/5) = 3ᵐ and find n from 5⁻¹⁰ ÷ 5⁻⁴ = 5ⁿ.

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Part (a) · 1 mark

Find the value of m in 3^(1/2) × 3^(2/5) = 3ᵐ.

  1. 13^(1/2) × 3^(2/5) = 3^(1/2 + 2/5)
  2. 21/2 + 2/5 = 5/10 + 4/10 = 9/10
  3. 3m = 9/10

Answer9/10

Part (b) · 1 mark

Find the value of n in 5⁻¹⁰ ÷ 5⁻⁴ = 5ⁿ.

  1. 15^(−10) ÷ 5^(−4) = 5^(−10 − (−4))
  2. 2−10 − (−4) = −10 + 4 = −6
  3. 3n = −6

Answer−6

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