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4024/12 Oct/Nov 2022, Question 17: Index Laws with Letters

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Three short index questions: simplify a power of a power, solve for t from a negative index, and find k in a surd and power equation.

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

Part (a) · 1 mark

Simplify the expression (x²)³, giving the result as a single power of x.

  1. 1(x²)³ = x^(2 × 3) = x⁶

Answerx⁶

Part (b) · 1 mark

Given t⁻² = 9, find the value of t.

  1. 1t⁻² = 1/t² = 9, so t² = 1/9
  2. 2t = ±1/3

Answer±1/3

Part (c) · 1 mark

Given √5 × 5⁰ = 5ᵏ, find the value of k.

  1. 1√5 = 5^(1/2) and 5⁰ = 1
  2. 25^(1/2) × 1 = 5ᵏ, so k = 1/2

Answer1/2

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