a^(1/n): Challenge & Extension
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties and applications of fractional indices a^(1/n), designed to challenge higher-level students with a variety of questions.
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a^(1/n): Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Date:
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify the expression: 8^(1/3).
[2 marks]2.
Calculate the value of: 16^(1/4).
[2 marks]3.
Express 125^(1/3) as a simplified number.
[2 marks]4.
If a = 81, find the value of a^(1/4).
[2 marks]5.
Calculate (27)^(2/3).
[3 marks]6.
Simplify: (64)^(3/6).
[2 marks]7.
Solve for x: x^(1/2) = 7.
[3 marks]8.
Express (125)^(1/3) in simplest form.
[2 marks]9.
A tower is 81 meters tall. Find the height if the height is proportional to the 4th root of a certain measurement: h = (measurement)^(1/4). If h=3, what is the measurement?
[4 marks]10.
Calculate the value of: (8)^(2/3).
[2 marks]11.
Construct a triangle on the grid with sides of lengths 8, 27, and a side of length (8)^(2/3). Show all working.
[4 marks]12.
Identify and correct the mistake in the following statement: 125^(1/3) = 5 and 125^(2/3) = 25.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet