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0580/23 Oct/Nov 2023, Question 17: Fractional Indices with Letters

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 4 marks

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The question, in short

Simplify two expressions: a power of 64y²⁷ raised to 2/3, and an algebraic fraction with x − 5 over x² − 25.

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

Part (a) · 2 marks

Simplify (64y²⁷)^(2/3), giving the result in its simplest form.

  1. 164^(2/3) = (∛64)² = 4² = 16
  2. 2(y²⁷)^(2/3) = y¹⁸
  3. 3= 16y¹⁸

Answer16y¹⁸

Part (b) · 2 marks

Simplify the fraction (x − 5)/(x² − 25).

  1. 1x² − 25 = (x + 5)(x − 5)
  2. 2(x − 5)/((x + 5)(x − 5)) = 1/(x + 5)

Answer1/(x + 5)

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Also searched as: 0580/23/O/N/23 · 0580_w23_qp_23 · 0580 w23 23 · question 17.
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