aᵐ × aⁿ = aᵐ⁺ⁿ: Real-world Applications
Mathematics
GCSE Foundation
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet explores the law aᵐ × aⁿ = aᵐ⁺ⁿ through real-world contexts related to art and patterns, helping students understand and apply the concept in practical situations.
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aᵐ × aⁿ = aᵐ⁺ⁿ: Real-world Applications
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Calculate each expression using the laws of indices. Show your working in the grid spaces provided.
1.
Simplify: 3³ × 3⁴
[2 marks]2.
Evaluate: 2² × 2⁵
[2 marks]3.
Express as a single power: a⁵ × a³
[2 marks]4.
Calculate: 5⁶ × 5²
[2 marks]B
Problem Solving & Reasoning
Solve these multi-step problems and explain your reasoning.
1.
A pattern uses squares with side lengths doubling each time. If the first pattern has side length a, what is the total area after three patterns if the areas are multiplied using indices?
[4 marks]2.
A designer creates tiles with patterns based on powers of 2. If one pattern uses 2² tiles and the next 2⁴ tiles, express the total number of tiles as a single power. Explain your steps.
[4 marks]C
Real-world Applications
Apply the laws of indices to real-world contexts involving art and pattern design.
1.
A mural uses a repeating pattern of tiles. Each tile's size doubles in each stage, starting from 1 m². After 4 stages, what is the total area of tiles used, expressed as a power of 2?
[3 marks]2.
An artist designs a fractal pattern where each iteration multiplies the number of smaller pattern units by 3. If they start with 3¹ units, how many units are there after 4 iterations? Express your answer as a power.
[3 marks]D
Challenge & Extension
Tackle these challenging problems and justify your answers.
1.
A pattern involves stacking layers of tiles, each layer doubling in number. If the first layer has 2² tiles, express the total number of tiles after 5 layers as a single power and explain the reasoning.
[4 marks]2.
In a fabric pattern, the number of motifs in each row doubles from the previous row. Starting with 2 motifs, how many motifs are in the 6th row? Express the answer as a power.
[3 marks]E
Mixed Review
Answer these questions to review different aspects of the law aᵐ × aⁿ = aᵐ⁺ⁿ.
1.
Express 7⁴ × 7² as a single power.
[2 marks]2.
If a³ × a⁵ = a⁸, what is the value of m in aᵐ? Show your working.
[3 marks]F
Error Analysis
Identify the mistake in each given calculation and correct it.
1.
A student writes: 4² × 4³ = 4⁵. Is this correct? If not, explain and correct the mistake.
[3 marks]2.
A student says: a³ × a² = a⁵, but writes the answer as a⁆. Find 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)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet