0580/23 Oct/Nov 2025, Question 12: Zero and Negative Indices
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 5 marks
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The question, in short
Evaluate powers and indices: a zero index, a negative index fraction, and express a product of powers of 3 in the form 3ⁿ.
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Part (a) · 1 mark
State the value of 73⁰.
- 1Any non-zero number to the power 0 is 1: 73⁰ = 1
Answer1
Part (b) · 2 marks
Calculate the value of 7 divided by 3⁻².
- 13⁻² = 1/9
- 27 ÷ 1/9 = 7 × 9 = 63
Answer63
Part (c) · 2 marks
Write 27 × 81² as 3ⁿ, giving the value of n.
- 127 = 3³ and 81² = (3⁴)² = 3⁸
- 227 × 81² = 3³⁺⁸ = 3¹¹
Answer3¹¹
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Also searched as: 0580/23/O/N/25 · 0580_w25_qp_23 · 0580 w25 23 · question 12.
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