Free Grade 3 Introducing Index Laws Flashcards
Free Grade 3 flashcards for Introducing Index Laws: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing index laws
Identify introducing index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing index laws
Explain introducing index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing index laws
Calculate introducing index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing index laws
Compare introducing index laws 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 Introducing Index Laws 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 7² and √49.[1]
- 2.Work out 9² and √81.[1]
- 3.Work out 10² and √100.[1]
- 4.Work out 3² and √9.[1]
- 5.Evaluate 3^3.[2]
- 6.Evaluate 2^4.[2]
- 7.Evaluate 3^4.[2]
- 8.Evaluate 5^4.[2]
- 9.Simplify x^4 × x^3 ÷ x^3.[3]
- 10.Simplify x^4 × x^3 ÷ x^6.[3]
- 11.Simplify x^7 × x^6 ÷ x^2.[3]
- 12.Simplify x^7 × x^3 ÷ x^3.[3]
Show answers and working
1. 49 and 7
7² = 7 × 7 = 49 √49 = 7 because 7 × 7 = 49
2. 81 and 9
9² = 9 × 9 = 81 √81 = 9 because 9 × 9 = 81
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. 27
Multiply 3 by itself 3 times. 3 × 3 × 3 = 27
6. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
7. 81
Multiply 3 by itself 4 times. 3 × 3 × 3 × 3 = 81
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^1
Multiplying: add the powers → x^7. Dividing: subtract the powers → x^7 ÷ x^6 = x^1.
11. x^11
Multiplying: add the powers → x^13. Dividing: subtract the powers → x^13 ÷ x^2 = x^11.
12. x^7
Multiplying: add the powers → x^10. Dividing: subtract the powers → x^10 ÷ x^3 = x^7.
Worked examples
Work out 8² and √64.
- 8² = 8 × 8 = 64
- √64 = 8 because 8 × 8 = 64
- Answer: 64 and 8
Evaluate 4^3.
- Multiply 4 by itself 3 times.
- 4 × 4 × 4 = 64
- Answer: 64
Simplify x^4 × x^3 ÷ x^4.
- Multiplying: add the powers → x^7.
- Dividing: subtract the powers → x^7 ÷ x^4 = x^3.
- Answer: x^3
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 Introducing Index Laws 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 Square Roots. 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 Introducing Index Laws?
- Move on to Working with Index Laws, Index Laws in Context, Squares, Cubes, which build directly on this idea.
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