aᵐ ÷ aⁿ = aᵐ⁻ⁿ: Challenge & Extension
Mathematics
GCSE Higher
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the law of indices aᵐ ÷ aⁿ = aᵐ⁻ⁿ, including procedural practice, reasoning, real-world applications, and extension challenges for GCSE Higher students.
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aᵐ ÷ aⁿ = aᵐ⁻ⁿ: Challenge & Extension
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 a³ ÷ a².
[2 marks]2.
Calculate the value of 5⁴ ÷ 5².
[2 marks]3.
Express as a single power: 2⁵ ÷ 2³.
[2 marks]4.
Simplify the expression 10⁶ ÷ 10⁴.
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Provide detailed explanations where required.
1.
Simplify the expression (a³b⁴) ÷ (a¹b²). Explain your steps.
[4 marks]2.
If 3⁸ ÷ 3⁵ = 3ˣ, find the value of x and explain why.
[3 marks]3.
A scientist models a phenomenon using 2⁸ ÷ 2ˣ. When the result is 2³, find x and justify your answer.
[4 marks]C
Real-world Applications
Answer all questions with detailed reasoning.
1.
A bacteria population doubles every hour. If the initial population is 1, model the population after x hours using powers of 2 and simplify the expression after dividing by 2².
[4 marks]D
Challenge & Extension
Attempt these advanced problems. Show detailed working.
1.
Simplify and evaluate (3⁷ ÷ 3³) × (3² ÷ 3¹).
[3 marks]2.
Express the division of powers with different bases, e.g., (a⁵b³) ÷ (a²b²), as simplified expressions, explaining your reasoning.
[4 marks]E
Mixed Review
Answer all questions. These test a variety of skills related to the law of indices.
1.
Simplify: (a¹⁰ ÷ a⁶) ÷ a².
[2 marks]2.
If a⁵ ÷ a⁻² = aˣ, find x.
[2 marks]3.
Simplify the expression: (2⁶ ÷ 2³) × 2⁴.
[2 marks]F
Error Analysis
Review the following mistake. Correct it and explain the error.
1.
A student simplifies a⁴ ÷ a² as a². Identify what went wrong and correct the mistake.
[3 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