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4MA1/2FR Jan 2022, Question 23: Laws of Indices

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 4 marks

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The question, in short

Apply index laws to evaluate x⁰, find n from 2⁻³ × 2⁹ = 2ⁿ, and find m from (7²⁰⁶ × 7ᵐ) ÷ 7²¹⁴ = 7⁻³.

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Part (a) · 1 mark

State the value of x⁰.

  1. 1x⁰ = 1 for any non-zero x

Answer1

Part (b) · 1 mark

Using 2⁻³ × 2⁹ = 2ⁿ, determine the value of n.

  1. 12⁻³ × 2⁹ = 2^(−3 + 9) = 2⁶
  2. 2n = 6

Answer6

Part (c) · 2 marks

Using (7²⁰⁶ × 7ᵐ) ÷ 7²¹⁴ = 7⁻³, determine the value of m.

  1. 17^(206 + m − 214) = 7⁻³
  2. 2206 + m − 214 = −3
  3. 3m − 8 = −3
  4. 4m = 5

Answer5

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