Simplify: x³ × x⁴.
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Indices II Topical Past Papers.
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These Indices II Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Algebra and graphs (E2.4) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Use indices (positive, zero, negative and fractional at Extended) in algebraic expressions and apply the rules of indices.
Simplify: x³ × x⁴.
Simplify: a⁵ ÷ a².
[1 mark]Simplify: (2y³)².
[2 marks]Simplify: (3x²y)³.
[2 marks]Find the value of x given that 2^x = 32.
Simplify: x^(3/2) × x^(1/2).
[1 mark]Find the exact value of 16^(3/4).
[2 marks]Simplify (2x³)^(−2). Give your answer with positive indices.
[2 marks]Find the value of x for which 8^x = 4^(x + 1).
[2 marks]