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4MA1/2FR Jun 2018, Question 21: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 6 marks

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The question, in short

Simplify three algebraic expressions involving indices and fractions, then rearrange a formula to make e the subject.

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

Part (a) · 1 mark

Simplify g⁷ × g³ by combining the powers of g.

  1. 1Multiplying powers of the same letter adds them: g⁷ × g³ = g^(7+3)
  2. 27 + 3 = 10, so the answer is g¹⁰

Answerg¹⁰

Part (b) · 1 mark

Simplify (k³)⁵ by applying the power rule to the index.

  1. 1A power of a power multiplies them: (k³)⁵ = k^(3 × 5)
  2. 23 × 5 = 15, so the answer is k¹⁵

Answerk¹⁵

Part (c) · 2 marks

Simplify the fraction (20x²y⁶)/(4x²y²) fully, giving the result in its simplest form.

  1. 1Divide the numbers: 20 ÷ 4 = 5
  2. 2Divide the x terms: x² ÷ x² = 1
  3. 3Divide the y terms: y⁶ ÷ y² = y^(6−2) = y⁴
  4. 4So the answer is 5y⁴

Answer5y⁴

Part (d) · 2 marks

Rearrange h = 3e + f to make e the subject of the formula.

  1. 1Subtract f from both sides: h − f = 3e
  2. 2Divide both sides by 3: e = (h − f)/3

Answer(h − f)/3

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