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4MA1/2HR Jan 2021, Question 19: Fractional Indices

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 7 marks

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The question, in short

Simplify 8² × ∛(4⁶) to a power of 2, showing stages, then solve n^(−4/5) = (1/2)⁴ for positive n.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Simplify 8² × ∛(4⁶) and express the result as 2^a with integer a, showing each stage.

  1. 18² = (2³)² = 2⁶
  2. 24⁶ = (2²)⁶ = 2¹², and a cube root divides the index by 3: ∛(2¹²) = 2⁴
  3. 3Multiply by adding indices: 2⁶ × 2⁴ = 2¹⁰

Answer2¹⁰

Part (b) · 4 marks

Given n^(−4/5) = (1/2)⁴ and n > 0, find the value of n.

  1. 1(1/2)⁴ = 2⁻⁴, so n^(−4/5) = 2⁻⁴
  2. 2Raise both sides to the power −5/4: n = (2⁻⁴)^(−5/4)
  3. 3n = 2⁵ = 32

Answern = 32

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