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4MA1/2F Jun 2018, Question 24: Laws of Indices

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

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The question, in short

Use index laws to find the unknown exponent in two equations involving powers of 2 and 13.

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

Part (a) · 2 marks

Find n where 8 divided by 2⁷ equals 2ⁿ.

  1. 18 = 2³, so the fraction is 2³ ÷ 2⁷
  2. 2Dividing powers subtracts them: 2^(3 − 7) = 2^(−4)
  3. 3So n = −4

Answer−4

Part (b) · 2 marks

Find k where (13⁻⁶)⁴ multiplied by 13⁵ equals 13ᵏ.

  1. 1(13⁻⁶)⁴ = 13^(−6 × 4) = 13⁻²⁴
  2. 213⁻²⁴ × 13⁵ = 13^(−24 + 5)
  3. 3−24 + 5 = −19, so k = −19

Answer−19

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