Lemmara logoLemmaraWorked solution

WMA11/01 Oct 2023, Question 2: Fractional Indices

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 4 marks

The question, in short

Given a = (1/64)x² and b = 16/√x, rewrite three expressions in the form kxⁿ with simplified constants k and n.

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

Part (a) · 1 mark

Express a^(1/2) in the form kxⁿ, simplifying the constant and exponent.

  1. 1a^(1/2) = (1/64)^(1/2) × (x²)^(1/2)
  2. 2= (1/8)x

Answer(1/8)x

Part (b) · 1 mark

Express 16/b³ in the form kxⁿ, simplifying the constant and exponent.

  1. 1b³ = 16³ × x^(−3/2) = 4096x^(−3/2)
  2. 216/b³ = 16/(4096x^(−3/2)) = (1/256)x^(3/2)

Answer(1/256)x^(3/2)

Part (c) · 2 marks

Express (ab/2)^(−4/3) in the form kxⁿ, simplifying the constant and exponent.

  1. 1ab = (1/64)x² × 16x^(−1/2) = (1/4)x^(3/2)
  2. 2ab/2 = (1/8)x^(3/2)
  3. 3(ab/2)^(−4/3) = (1/8)^(−4/3) × x^(−2)
  4. 4(1/8)^(−4/3) = 8^(4/3) = 16, so the answer is 16x⁻²

Answer16x⁻²

Stuck on a step? Read the free lesson: Fractional Indices

Practise more fractional indices questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on fractional indices

Also searched as: WMA11 October 2023 · WMA11/01 · wma11 oct23 · IAS Maths Pure Mathematics 1 October 2023 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.