0580/22 Feb/Mar 2022, Question 13: Index Laws with Letters

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

The question, in short

Three short index-law exercises: combine a product of powers of h, rewrite a negative power of a fraction, and use a division of powers of a to determine p.

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

Part (a) · 1 mark

Write h² multiplied by h⁵ as a single power of h.

1h² × h⁵ = h²⁺⁵ = h⁷

Answerh⁷

Part (b) · 1 mark

Express (7/x)⁻³ in a form without a negative index.

1(7/x)⁻³ = (x/7)³ = x³/343

Answerx³/343

Part (c) · 1 mark

Given a⁸ divided by aᵖ equals a², work out the number p.

1a⁸ ÷ aᵖ = a⁸⁻ᵖ = a²
28 − p = 2, so p = 6

Answer6

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