Free Grade 3 Working with Differentiating Powers Flashcards
Free Grade 3 flashcards for Working with Differentiating Powers: 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
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with differentiating powers
Explain working with differentiating powers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with differentiating powers
Calculate working with differentiating powers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with differentiating powers
Compare working with differentiating powers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with differentiating powers
Justify working with differentiating powers 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 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 6² and √36.[1]
- 2.Work out 3² and √9.[1]
- 3.Work out 7² and √49.[1]
- 4.Work out 12² and √144.[1]
- 5.Evaluate 5^3.[2]
- 6.Evaluate 2^3.[2]
- 7.Evaluate 4^4.[2]
- 8.Evaluate 5^4.[2]
- 9.Simplify x^4 × x^3 ÷ x^3.[3]
- 10.Simplify x^3 × x^6 ÷ x^4.[3]
- 11.Simplify x^3 × x^5 ÷ x^2.[3]
- 12.Simplify x^2 × x^4 ÷ x^3.[3]
Show answers and working
1. 36 and 6
6² = 6 × 6 = 36 √36 = 6 because 6 × 6 = 36
2. 9 and 3
3² = 3 × 3 = 9 √9 = 3 because 3 × 3 = 9
3. 49 and 7
7² = 7 × 7 = 49 √49 = 7 because 7 × 7 = 49
4. 144 and 12
12² = 12 × 12 = 144 √144 = 12 because 12 × 12 = 144
5. 125
Multiply 5 by itself 3 times. 5 × 5 × 5 = 125
6. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
7. 256
Multiply 4 by itself 4 times. 4 × 4 × 4 × 4 = 256
8. 625
Multiply 5 by itself 4 times. 5 × 5 × 5 × 5 = 625
9. x^4
Multiplying: add the powers → x^7. Dividing: subtract the powers → x^7 ÷ x^3 = x^4.
10. x^5
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^4 = x^5.
11. x^6
Multiplying: add the powers → x^8. Dividing: subtract the powers → x^8 ÷ x^2 = x^6.
12. x^3
Multiplying: add the powers → x^6. Dividing: subtract the powers → x^6 ÷ x^3 = x^3.
Worked examples
Work out 11² and √121.
- 11² = 11 × 11 = 121
- √121 = 11 because 11 × 11 = 121
- Answer: 121 and 11
Evaluate 2^4.
- Multiply 2 by itself 4 times.
- 2 × 2 × 2 × 2 = 16
- Answer: 16
Simplify x^2 × x^6 ÷ x^3.
- Multiplying: add the powers → x^8.
- Dividing: subtract the powers → x^8 ÷ x^3 = 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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Frequently asked
- Is this Grade 3 Working with Differentiating Powers flashcards really free?
- Yes. Every flashcards 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 Introducing Differentiating Powers, Rate of Change. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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?
- Move on to Differentiating Powers in Context, Rate of Change, Tangents and Normals, Stationary Points, which build directly on this idea.
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