a⁻ⁿ = 1/aⁿ: Error Analysis & Misconceptions
Mathematics
Grade 6
15 questions
~30 mins
1 views0 downloads
About This Worksheet
This worksheet explores the concept of negative indices, focusing on the key formula a⁻ⁿ = 1/aⁿ. It helps students identify common errors and deepen their understanding.
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a⁻ⁿ = 1/aⁿ: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Introduction
Read the explanation below to understand the key concept.
1.
The rule a⁻ⁿ = 1/aⁿ means that a negative exponent indicates a reciprocal. Explain in your own words what this rule tells us about negative powers.
[2 marks]B
Fluency & Practice
Answer the following questions to practice applying the rule a⁻ⁿ = 1/aⁿ.
1.
Calculate 2⁻³.
[2 marks]2.
Evaluate 5⁻².
[2 marks]3.
Simplify 10⁻¹.
[2 marks]4.
Calculate 3⁻⁴.
[2 marks]C
Error Analysis & Misconceptions
The following questions include common mistakes. Identify and correct the errors.
1.
A student writes: 4⁻² = 4². Is this correct? Explain and correct the mistake if needed.
[3 marks]2.
Identify the mistake in: 7⁻³ = 7³.
[3 marks]D
Problem Solving & Reasoning
Solve these multi-step problems involving negative indices and explain your reasoning.
1.
Simplify (2/3)⁻² and explain why your answer makes sense.
[3 marks]2.
If a⁻⁴ = 1/16, what is the value of a? Show your working.
[3 marks]E
Real-world Applications
Apply the rule a⁻ⁿ = 1/aⁿ to real-world contexts.
1.
A scientist records the concentration of a substance as 5⁻¹ mol/L. What is the concentration in simpler form? Explain your reasoning.
[3 marks]F
Challenge & Extension
Tackle these more advanced problems to extend your understanding.
1.
Prove that (a/b)⁻ⁿ = (b/a)ⁿ using the rule a⁻ⁿ = 1/aⁿ.
[4 marks]2.
If 9⁻ᵏ = 1/81, find the value of k and explain your reasoning.
[3 marks]G
Mixed Review & Final Challenge
Review different aspects of negative indices with these questions.
1.
Express 1/8 as a negative power of 2.
[2 marks]2.
Construct a small diagram on the grid to show the reciprocal relationship between 4³ and 4⁻³.
[3 marks]3.
Identify and correct the mistake: 6⁻² = 6².
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet