aᵐ × aⁿ = aᵐ⁺ⁿ: Challenge & Extension
Mathematics
GCSE Foundation
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the law of indices aᵐ × aⁿ = aᵐ⁺ⁿ through fluency, problem solving, real-world contexts, and challenging extension questions.
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aᵐ × aⁿ = aᵐ⁺ⁿ: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of 2³ × 2⁴.
[2 marks]2.
Simplify the expression a⁵ × a³.
[2 marks]3.
Express as a single power: 3² × 3⁵.
[2 marks]4.
Compute the value of 5⁴ × 5².
[2 marks]B
Problem Solving & Reasoning
Show detailed working for each question.
1.
If aˣ × aʸ = aᶻ, and a = 2, x = 3, y = 5, find the value of z.
[3 marks]2.
A scientist is working with a substance that reduces in quantity by a factor of a² each hour. If the initial quantity is Q, write an expression for the quantity after t hours, using indices, and simplify.
[4 marks]C
Real-world Applications
Use the grid to diagram or calculate as necessary.
1.
A bacteria culture doubles in size every hour. If its initial size is 1, express the size after t hours as an exponential expression using indices, and find its size after 4 hours.
[3 marks]D
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
Simplify the expression (a²b³) × (a⁴b²), assuming a and b are variables.
[3 marks]2.
Given that x = 2 and y = 3, evaluate (x³ y²) × (x² y⁴).
[3 marks]E
Mixed Review
Solve these questions to reinforce your understanding.
1.
Write as a single power: 4¹ × 4³ × 4².
[2 marks]2.
Simplify the expression a⁰ × a³.
[2 marks]F
Error Analysis
Identify and correct the mistake in each error question.
1.
A student wrote: a² × a⁴ = a⁸. Is this correct? If not, explain and correct the mistake.
[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