4MA1/1HR Jun 2019, Question 20: Fractional Indices
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
Given a = 25 × 10¹⁴ⁿ with n an integer, find an expression for a^(3/2) in terms of n, giving the answer in standard form.
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Solution · 3 marks
- 1a = 25 × 10¹⁴n
- 2a^(3/2) = (25)^(3/2) × (10¹⁴n)^(3/2)
- 325^(3/2) = (√25)³ = 5³ = 125
- 4(10¹⁴n)^(3/2) = 10^(14n × 3/2) = 10^(21n)
- 5125 × 10²¹n
- 6125 = 1.25 × 10²
- 71.25 × 10² × 10²¹n = 1.25 × 10^(21n + 2)
Answer1.25 × 10²¹ⁿ⁺²
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