4MA1/2H Jun 2024, Question 23: Laws of Indices
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Simplify the expression (30 × 25²ˣ⁺⁷) ÷ (√180 × (√5)⁴ˣ⁺⁹) to the form 5ʷ, showing each stage of working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 125 = 5², so 25^(2x+7) = 5^(2(2x+7)) = 5^(4x+14)
- 230 = 6 × 5, so the numerator = 6 × 5 × 5^(4x+14) = 6 × 5^(4x+15)
- 3√180 = √(36 × 5) = 6√5 = 6 × 5^(1/2)
- 4(√5)^(4x+9) = (5^(1/2))^(4x+9) = 5^(2x+4.5)
- 5so the denominator = 6 × 5^(1/2) × 5^(2x+4.5) = 6 × 5^(2x+5)
- 6(6 × 5^(4x+15)) ÷ (6 × 5^(2x+5)) = 5^((4x+15) − (2x+5))
- 7= 5^(2x+10), so w = 2x + 10
Answer5²ˣ⁺¹⁰
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