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0580/23 May/Jun 2026, Question 22: Zero and Negative Indices with Letters

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 6 marks

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The question, in short

Simplify two index expressions and solve an equation with powers to find n.

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

Part (ai) · 2 marks

Simplify (10b⁴)⁻³, giving the result with a negative or positive index.

  1. 1(10b⁴)⁻³ = 10⁻³ b⁻¹²
  2. 2= 1/(1000b¹²)

Answer1/(1000b¹²)

Part (aii) · 2 marks

Simplify (8p¹⁵)^(2/3) using fractional index rules.

  1. 18^(2/3) = (∛8)² = 2² = 4
  2. 2(p¹⁵)^(2/3) = p¹⁰
  3. 34p¹⁰

Answer4p¹⁰

Part (b) · 2 marks

Given 16ⁿ = 64, find the value of n.

  1. 116 = 2⁴ and 64 = 2⁶
  2. 22⁴ⁿ = 2⁶
  3. 34n = 6
  4. 4n = 3/2

Answer3/2

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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 22.
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