Free Grade 3 Working with Introducing Differentiating Powers Common Errors Quizzes
Free Grade 3 quizzes for Working with Introducing 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with introducing differentiating powers common errors
Identify working with introducing differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with introducing differentiating powers common errors
Explain working with introducing differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing differentiating powers common errors
Calculate working with introducing differentiating powers common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing differentiating powers common errors
Compare working with introducing 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 Introducing 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 4² and √16.[1]
- 3.Work out 8² and √64.[1]
- 4.Work out 7² and √49.[1]
- 5.Evaluate 4^3.[2]
- 6.Evaluate 3^3.[2]
- 7.Evaluate 2^3.[2]
- 8.Evaluate 2^4.[2]
- 9.Simplify x^7 × x^2 ÷ x^3.[3]
- 10.Simplify x^3 × x^5 ÷ x^5.[3]
- 11.Simplify x^6 × x^3 ÷ x^5.[3]
- 12.Simplify x^2 × x^6 ÷ x^6.[3]
Show answers and working
1. 25 and 5
5² = 5 × 5 = 25 √25 = 5 because 5 × 5 = 25
2. 16 and 4
4² = 4 × 4 = 16 √16 = 4 because 4 × 4 = 16
3. 64 and 8
8² = 8 × 8 = 64 √64 = 8 because 8 × 8 = 64
4. 49 and 7
7² = 7 × 7 = 49 √49 = 7 because 7 × 7 = 49
5. 64
Multiply 4 by itself 3 times. 4 × 4 × 4 = 64
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. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
9. x^6
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^3 = x^6.
10. x^3
Multiplying: add the powers → x^8. Dividing: subtract the powers → x^8 ÷ x^5 = x^3.
11. x^4
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^5 = x^4.
12. x^2
Multiplying: add the powers → x^8. Dividing: subtract the powers → x^8 ÷ x^6 = x^2.
Worked examples
Work out 9² and √81.
- 9² = 9 × 9 = 81
- √81 = 9 because 9 × 9 = 81
- Answer: 81 and 9
Evaluate 5^3.
- Multiply 5 by itself 3 times.
- 5 × 5 × 5 = 125
- Answer: 125
Simplify x^5 × x^6 ÷ x^6.
- Multiplying: add the powers → x^11.
- Dividing: subtract the powers → x^11 ÷ x^6 = x^5.
- Answer: x^5
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.
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- Start with Rules and Methods in Introducing Differentiating Powers Common Errors, Key Vocabulary of Introducing Differentiating Powers Common Errors, Introducing Differentiating Powers Word Problems. Each one has its own free lesson, worksheet and quiz.
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