aᵐ × aⁿ = aᵐ⁺ⁿ: Error Analysis & Misconceptions
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring common errors and misconceptions related to the law of indices aᵐ × aⁿ = aᵐ⁺ⁿ, with practice and reasoning questions.
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aᵐ × aⁿ = aᵐ⁺ⁿ: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concept below before attempting the questions.
1.
The law of indices for multiplication states that aᵐ × aⁿ = aᵐ⁺ⁿ, provided that a ≠ 0. This rule allows us to simplify expressions involving powers of the same base.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate a² × a³.
[2 marks]2.
Simplify the expression a⁴ × a².
[2 marks]3.
Evaluate a⁰ × a².
[2 marks]C
Problem Solving & Reasoning
Solve the following problems and explain your reasoning clearly.
1.
If a = 2, what is the value of a² × a³? Explain your steps.
[3 marks]2.
Given that a ≠ 0, if a³ × a⁻¹ = a², is this correct? Justify your answer.
[3 marks]D
Real-world Applications
Apply the law of indices to solve the following contextual problems.
1.
A bacterial population doubles every hour, described by P = P₀ × 2^t, where t is hours. Rewrite P in terms of powers of 2 and explain the process.
[3 marks]E
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
Simplify (a²b) × (a³b²), assuming a and b are non-zero variables. Comment on any misconceptions related to the law of indices.
[3 marks]2.
Identify and correct the mistake in the following: a⁴ × a⁻² = a².
[2 marks]F
Mixed Review & Error Analysis
Identify errors in the following and correct them.
1.
Error: a² × a⁴ = a⁶. Is this correct? If not, explain and give the correct answer.
[2 marks]2.
A student writes: a³ × a⁻² = a¹. Is this correct? Justify your answer.
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet