4MA1/2HR Jun 2019, Question 14: Fractional Indices with Letters
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Reduce the power expression (x¹²y⁸)^(3/4) to its simplest form, then use 3ⁿ = 3ˣ/9ʸ to express n using x and y.
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Part (a) · 2 marks
Write (x¹²y⁸)^(3/4) in its simplest form.
- 1Raise each power to 3/4: multiply the indices by 3/4
- 2x: 12 × 3/4 = 9; y: 8 × 3/4 = 6
- 3x⁹y⁶
Answerx⁹y⁶
Part (b) · 2 marks
Starting from 3ⁿ = 3ˣ/9ʸ, derive n as an expression involving x and y.
- 1Write 9 as a power of 3: 9ʸ = (3²)ʸ = 3²ʸ
- 23ˣ ÷ 3²ʸ = 3ˣ⁻²ʸ
- 3n = x − 2y
Answern = x − 2y
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