0580/32 Feb/Mar 2025, Question 17: Zero and Negative Indices with Letters
Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 4 marks
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The question, in short
Solve three short algebra items: an equation for x, an index equation for y, and simplify an algebraic fraction with powers.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 1 mark
Solve x/3 = 18 to find x.
- 1x = 18 × 3 = 54
Answer54
Part (b) · 1 mark
Given 6⁹ ÷ 6ʸ = 6¹¹, find the value of y.
- 16⁹⁻ʸ = 6¹¹, so 9 − y = 11, y = −2
Answer−2
Part (c) · 2 marks
Simplify (a⁶b⁻²)/(a⁴b³), giving the result with powers.
- 1a⁶⁻⁴ = a² and b⁻²⁻³ = b⁻⁵
- 2= a²b⁻⁵ = a²/b⁵
Answera²/b⁵ or a²b⁻⁵
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