EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Zero, Negative and Fractional Indices
Zero, negative and fractional indices · Number · Lesson 5 of 7 · 10 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [1 mark]
Write down the value of 7⁰.
Question 2 NON-CALCULATOR [1 mark]
Write 4⁻² as a fraction.
Question 3 NON-CALCULATOR · HIGHER [1 mark]
Write down the value of 64^(1/2).
Question 4 NON-CALCULATOR · HIGHER [2 marks]
Find the value of 125^(−2/3).
Question 5 NON-CALCULATOR · HIGHER [2 marks]
Find the value of (27/8)^(−2/3).
Question 6 NON-CALCULATOR · HIGHER [3 marks]
Write √8 × 4⁻³ as a single power of 2.
Answers
Check your answer only once you have written one.
Question 1 [1 mark]
1
▸ 1 B1
Question 2 [1 mark]
1/16
▸ 1/16 B1
Question 3 [1 mark]
8
▸ 8 B1
Question 4 [2 marks]
125^(−2/3) = 1/(125^(2/3)). ∛125 = 5 and 5² = 25, so the answer is 1/25.
▸ 1/(125^(2/3)), or ∛125 = 5, or 25 seen M1
▸ 1/25 A1
Question 5 [2 marks]
Flip: (8/27)^(2/3). Cube root: ⅔. Square: 4/9.
▸ (8/27)^(2/3), or 3/2 or ⅔ seen M1
▸ 4/9 A1
Question 6 [3 marks]
√8 = 8^(1/2) = (2³)^(1/2) = 2^(3/2). 4⁻³ = (2²)⁻³ = 2⁻⁶. 2^(3/2) × 2⁻⁶ = 2^(3/2 − 6) = 2^(−9/2).
▸ √8 written as 2^(3/2) M1
▸ 4⁻³ written as 2⁻⁶ M1
▸ 2^(−9/2) A1