Free Grade 3 Differentiating Powers in Context Common Errors Worksheets
Free Grade 3 worksheets for Differentiating Powers in Context 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
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain differentiating powers in context common errors
Explain differentiating powers in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate differentiating powers in context common errors
Calculate differentiating powers in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare differentiating powers in context common errors
Compare differentiating powers in context common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify differentiating powers in context common errors
Justify differentiating powers in context 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 Differentiating Powers in Context 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 12² and √144.[1]
- 3.Work out 4² and √16.[1]
- 4.Work out 3² and √9.[1]
- 5.Evaluate 3^3.[2]
- 6.Evaluate 5^4.[2]
- 7.Evaluate 2^4.[2]
- 8.Evaluate 2^3.[2]
- 9.Simplify x^6 × x^5 ÷ x^6.[3]
- 10.Simplify x^7 × x^3 ÷ x^3.[3]
- 11.Simplify x^6 × x^7 ÷ x^5.[3]
- 12.Simplify x^5 × x^4 ÷ x^5.[3]
Show answers and working
1. 25 and 5
5² = 5 × 5 = 25 √25 = 5 because 5 × 5 = 25
2. 144 and 12
12² = 12 × 12 = 144 √144 = 12 because 12 × 12 = 144
3. 16 and 4
4² = 4 × 4 = 16 √16 = 4 because 4 × 4 = 16
4. 9 and 3
3² = 3 × 3 = 9 √9 = 3 because 3 × 3 = 9
5. 27
Multiply 3 by itself 3 times. 3 × 3 × 3 = 27
6. 625
Multiply 5 by itself 4 times. 5 × 5 × 5 × 5 = 625
7. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
8. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
9. x^5
Multiplying: add the powers → x^11. Dividing: subtract the powers → x^11 ÷ x^6 = x^5.
10. x^7
Multiplying: add the powers → x^10. Dividing: subtract the powers → x^10 ÷ x^3 = x^7.
11. x^8
Multiplying: add the powers → x^13. Dividing: subtract the powers → x^13 ÷ x^5 = x^8.
12. x^4
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^5 = x^4.
Worked examples
Work out 2² and √4.
- 2² = 2 × 2 = 4
- √4 = 2 because 2 × 2 = 4
- Answer: 4 and 2
Evaluate 4^4.
- Multiply 4 by itself 4 times.
- 4 × 4 × 4 × 4 = 256
- Answer: 256
Simplify x^7 × x^5 ÷ x^5.
- Multiplying: add the powers → x^12.
- Dividing: subtract the powers → x^12 ÷ x^5 = x^7.
- Answer: x^7
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
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Frequently asked
- Is this Grade 3 Differentiating Powers in Context 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 Differentiating Powers in Context Word Problems, Differentiating Powers in Context Techniques, Working with 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 Differentiating Powers in Context Common Errors?
- Move on to Introducing Differentiating Powers, Working with Differentiating Powers, which build directly on this idea.
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