a^(m/n): Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties and applications of fractional indices a^(m/n), designed to challenge and extend Grade 8 students' understanding.
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a^(m/n): Challenge & Extension
Subject: MathematicsGrade: Grade 8
Name:
Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of 8^(2/3).
[2 marks]2.
Simplify (16)^(3/4).
[2 marks]3.
Express 81^(1/4) as a simplified radical.
[2 marks]B
Problem Solving & Reasoning
Show detailed working for each problem.
1.
If a = 16, evaluate a^(3/4) and explain what the fractional exponent represents.
[3 marks]2.
Solve for x: (x^2)^(3/2) = 64. Show your working.
[3 marks]C
Real-world Applications
Apply your understanding to the context provided.
1.
A gardener plants a tree such that its growth follows the model height = 2^(t/3), where t is time in years. How tall will the tree be after 9 years?
[3 marks]D
Challenge & Extension
Tackle these advanced problems. Show all your reasoning.
1.
Prove that (27)^(2/3) = 9 by expressing 27 as a power of 3 and simplifying.
[3 marks]2.
If a^(m/n) = b and a = 16, find possible values of m and n if b = 2, and justify your answer.
[3 marks]E
Mixed Review
Answer these questions to reinforce your understanding.
1.
Calculate (125)^(3/3).
[2 marks]2.
Express 32^(5/5) as a simple number.
[2 marks]F
Error Analysis
Identify and correct the common mistake in the following problem.
1.
A student calculates (64)^(1/2) as 8. Is this correct? If not, explain and correct the mistake.
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet