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0580/22 Feb/Mar 2024, Question 21: Index Laws with Letters

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Two short algebra tasks: find the exponent h in a fifth-root equation, and simplify a cubed expression involving 4x³.

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

Part (a) · 1 mark

Given fifth root of 3 equals 3 to the power h, state the value of h.

  1. 1⁵√3 = 3^(1/5)
  2. 2h = 1/5

Answer1/5

Part (b) · 2 marks

Simplify the expression (4x³)³, giving the result in its simplest form.

  1. 1Cube each part of the bracket: 4³ and (x³)³.
  2. 24³ = 4 × 4 × 4 = 64
  3. 3(x³)³ = x⁹ (multiply the powers: 3 × 3 = 9)
  4. 4(4x³)³ = 64x⁹

Answer64x⁹

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