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4024/12 May/Jun 2021, Question 16: Fractional Indices with Letters

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Solve for k in the index equation (yᵏ)⁻² = y⁵, then simplify the expression (x^(1/3)/(2x))³.

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

Part (a) · 1 mark

Find the value of k that makes (yᵏ)⁻² equal y⁵.

  1. 1(yᵏ)⁻² = y⁻²ᵏ
  2. 2−2k = 5
  3. 3k = −5/2

Answer−5/2

Part (b) · 2 marks

Simplify (x^(1/3)/(2x))³, giving the result in its simplest index form.

  1. 1x^(1/3) ÷ 2x = x^(−2/3)/2
  2. 2(x^(−2/3)/2)³ = x⁻²/8
  3. 3= 1/(8x²)

Answer1/(8x²) or (1/8)x⁻²

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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 16.
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