(aᵐ)ⁿ = aᵐⁿ: Problem Solving & Reasoning
Mathematics
GCSE Higher
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the law (aᵐ)ⁿ = aᵐⁿ through practice, problem solving, real-world applications, and extension questions for GCSE Higher students.
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(aᵐ)ⁿ = aᵐⁿ: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify the expression (3³)⁴.
[2 marks]2.
Calculate the value of (2⁵)³.
[2 marks]3.
Express (5²)⁶ as a single power of 5.
[2 marks]4.
Simplify (7⁴)².
[2 marks]B
Practice & Application
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify (x³)⁵ where x ≠ 0.
[2 marks]2.
Express (a²b³)⁴ as a product of powers of a and b.
[3 marks]3.
Simplify (x⁴)³ + (x²)⁶.
[3 marks]4.
If (a³)² = 64, find the value of a.
[3 marks]5.
Express (x⁵)⁻³ as a power of x.
[2 marks]C
Real-world Application
Answer all questions. Show your working in the grid spaces provided.
1.
A scientist models the growth of bacteria with the expression (2³)⁵. How many bacteria are modeled after 5 time units?
[3 marks]D
Challenge & Extension
Answer all questions. Show your working in the grid spaces provided.
1.
Given that (a²)³ = 64 and a ≠ 0, find the value of a and verify your answer using the law of indices.
[4 marks]2.
Construct an expression with powers of different bases that simplifies to x⁹ using the law (aᵐ)ⁿ = aᵐⁿ.
[4 marks]E
Mixed Review & Error Analysis
Answer all questions. Identify common mistakes where needed.
1.
Simplify (2⁴)³ + (2³)⁴ and explain if they are equal.
[3 marks]2.
A student simplifies (x⁵)² as x¹⁰ but forgets the power of power law. Identify the mistake and correct it.
[4 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