(aᵐ)ⁿ = aᵐⁿ: Real-world Applications
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the law (aᵐ)ⁿ = aᵐⁿ through real-world contexts and mathematical practice, suitable for Year 9 students.
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(aᵐ)ⁿ = aᵐⁿ: Real-world Applications
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of (3²)³.
[2 marks]2.
Simplify (5⁴)².
[2 marks]3.
Evaluate (2³)⁴.
[2 marks]4.
Calculate (7¹)⁵.
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step questions, explaining your reasoning clearly.
1.
A square has side length represented by 2³ meters. Find the expression for the area of the square raised to the power 4, and simplify.
[4 marks]2.
A scientist doubles the concentration of a solution (represented as a¹) three times, each time applying the law (aᵐ)ⁿ. Write the resulting expression and simplify.
[4 marks]3.
A computer's processing power is proportional to (2²)⁵. Write the expression and find its simplified form.
[2 marks]C
Real-world Applications
Solve these contextual problems using the laws of indices.
1.
An organism's population doubles every year, starting from 1, represented as 2¹. Write an expression for the population after n years and simplify using laws of indices.
[3 marks]2.
A factory's output is proportional to (5³) raised to the power 2, representing two phases of production. Write and simplify the expression.
[3 marks]D
Challenge & Extension
Attempt these advanced problems. Show detailed working.
1.
Express ((4²)³)⁴ as a single power of 4 and simplify.
[4 marks]2.
A cube's volume is proportional to (3³)³. Write the expression and simplify, then interpret in a real-world context.
[4 marks]E
Mixed Review
Solve these questions to reinforce understanding of (aᵐ)ⁿ = aᵐⁿ.
1.
Simplify (6⁴)³.
[2 marks]2.
Express (x²)³ in terms of x and simplify.
[2 marks]F
Error Analysis
Identify and correct the mistake in the student's solution.
1.
Student's solution: (a³)⁴ = a⁷. Find and explain 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