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4MA1/1FR Jun 2023, Question 22: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 4 marks

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The question, in short

Simplify index expressions: divide powers of m, find n from a product of powers of k, and square a product with coefficients and two variables.

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

Part (a) · 1 mark

Simplify m to the power 10 divided by m cubed.

  1. 1m¹⁰ ÷ m³ = m^(10-3)
  2. 2m⁷

Answerm⁷

Part (b) · 1 mark

Given k to the n times k to the 4 equals k to the 12, state the value of n.

  1. 1kⁿ × k⁴ = k^(n+4)
  2. 2k^(n+4) = k¹²
  3. 3n + 4 = 12
  4. 4n = 8

Answer8

Part (c) · 2 marks

Simplify the square of 3x to the 6 y to the 8.

  1. 1(3x⁶ y⁸)² = 3² × (x⁶)² × (y⁸)²
  2. 29 × x¹² × y¹⁶
  3. 39x¹²y¹⁶

Answer9x¹²y¹⁶

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