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0580/21 May/Jun 2021, Question 11: Index Laws with Letters

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks

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The question, in short

Simplify a power of a product, solve an equation with a fractional index, and find an exponent from a division equation.

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

Part (a) · 2 marks

Simplify fully the expression (4ab⁵)⁴.

  1. 14⁴ = 256
  2. 2(a)⁴ = a⁴ and (b⁵)⁴ = b²⁰
  3. 3= 256a⁴b²⁰

Answer256a⁴b²⁰

Part (b) · 1 mark

Given 2p^(1/3) = 6, find the value of p.

  1. 1p^(1/3) = 6 ÷ 2 = 3
  2. 2p = 3³ = 27

Answer27

Part (c) · 2 marks

Given 81² ÷ 3ᵗ = 9, find the value of t.

  1. 181² = (3⁴)² = 3⁸ and 9 = 3²
  2. 23⁸ ÷ 3ᵗ = 3²
  3. 38 − t = 2
  4. 4t = 6

Answer6

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