Free Grade 3 Working with Differentiating Powers Common Errors Worksheets
Free Grade 3 worksheets for Working with Differentiating Powers Common Errors: 12 real questions with a full answer key and worked solutions. A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
Free
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with differentiating powers common errors
Explain working with differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with differentiating powers common errors
Calculate working with differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with differentiating powers common errors
Compare working with differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with differentiating powers common errors
Justify working with differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Differentiating Powers Common Errors works
A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Work out 5² and √25.[1]
- 2.Work out 11² and √121.[1]
- 3.Work out 10² and √100.[1]
- 4.Work out 3² and √9.[1]
- 5.Evaluate 4^4.[2]
- 6.Evaluate 3^3.[2]
- 7.Evaluate 2^3.[2]
- 8.Evaluate 5^4.[2]
- 9.Simplify x^3 × x^6 ÷ x^6.[3]
- 10.Simplify x^6 × x^6 ÷ x^2.[3]
- 11.Simplify x^7 × x^6 ÷ x^3.[3]
- 12.Simplify x^3 × x^2 ÷ x^6.[3]
Show answers and working
1. 25 and 5
5² = 5 × 5 = 25 √25 = 5 because 5 × 5 = 25
2. 121 and 11
11² = 11 × 11 = 121 √121 = 11 because 11 × 11 = 121
3. 100 and 10
10² = 10 × 10 = 100 √100 = 10 because 10 × 10 = 100
4. 9 and 3
3² = 3 × 3 = 9 √9 = 3 because 3 × 3 = 9
5. 256
Multiply 4 by itself 4 times. 4 × 4 × 4 × 4 = 256
6. 27
Multiply 3 by itself 3 times. 3 × 3 × 3 = 27
7. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
8. 625
Multiply 5 by itself 4 times. 5 × 5 × 5 × 5 = 625
9. x^3
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^6 = x^3.
10. x^10
Multiplying: add the powers → x^12. Dividing: subtract the powers → x^12 ÷ x^2 = x^10.
11. x^10
Multiplying: add the powers → x^13. Dividing: subtract the powers → x^13 ÷ x^3 = x^10.
12. x^-1
Multiplying: add the powers → x^5. Dividing: subtract the powers → x^5 ÷ x^6 = x^-1.
Worked examples
Work out 9² and √81.
- 9² = 9 × 9 = 81
- √81 = 9 because 9 × 9 = 81
- Answer: 81 and 9
Evaluate 3^4.
- Multiply 3 by itself 4 times.
- 3 × 3 × 3 × 3 = 81
- Answer: 81
Simplify x^6 × x^7 ÷ x^5.
- Multiplying: add the powers → x^13.
- Dividing: subtract the powers → x^13 ÷ x^5 = x^8.
- Answer: x^8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Works out 3² as 6.
Correction: 3² means 3 × 3, not 3 × 2.
Multiplies indices when multiplying powers.
Correction: x³ × x⁴ = x⁷ — add, don't multiply.
Teacher tips
- · Write powers out in full before using index laws.
Parent tips
- · Spot square numbers on tiles or a chessboard.
Real-life applications
- · Area in square units, computer storage (powers of 2).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Differentiating Powers Common Errors
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with Differentiating Powers Common Errors worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Differentiating Powers Word Problems, Working with Differentiating Powers Techniques, Introducing Differentiating Powers. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Differentiating Powers Common Errors?
- Move on to Introducing Differentiating Powers, Differentiating Powers in Context, which build directly on this idea.
Related resources
- Free Working with Differentiating Powers Common Errors quizzes
- Free Working with Differentiating Powers Common Errors flashcards
- Free Working with Differentiating Powers Common Errors lessons
- Free Working with Differentiating Powers Common Errors lesson plans
- Working with Differentiating Powers Common Errors in the knowledge graph
- Free AI Tutor
Stuck on Working with Differentiating Powers Common Errors? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor