Lemmara logoLemmaraWorked solution

0580/13 May/Jun 2025, Question 17: Index Laws with Letters

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 3 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Simplify three separate algebraic expressions involving powers of y, p and w, giving each result in its simplest index form.

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

Part (a) · 1 mark

Simplify y⁴ × y⁶ by combining the indices.

  1. 1y⁴ × y⁶ = y⁴⁺⁶ = y¹⁰

Answery¹⁰

Part (b) · 1 mark

Simplify p⁵ ÷ p⁸, giving the result with a single index.

  1. 1p⁵/p⁸ = p⁵⁻⁸ = p⁻³ = 1/p³

Answerp⁻³ or 1/p³

Part (c) · 1 mark

Simplify (w⁴)³ by raising the power to a power.

  1. 1Power of a power: multiply the indices, 4 × 3 = 12
  2. 2(w⁴)³ = w¹²

Answerw¹²

Stuck on a step? Read the free lesson: Index Laws with Letters

Practise more index laws with letters questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on index laws with letters

Also searched as: 0580/13/M/J/25 · 0580_s25_qp_13 · 0580 s25 13 · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.