Free Grade 3 Index Laws Worksheets
Free Grade 3 worksheets for 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify index laws
Identify index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain index laws
Explain index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate index laws
Calculate index laws accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare index laws
Compare 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 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 11² and √121.[1]
- 2.Work out 8² and √64.[1]
- 3.Work out 2² and √4.[1]
- 4.Work out 7² and √49.[1]
- 5.Evaluate 5^4.[2]
- 6.Evaluate 2^3.[2]
- 7.Evaluate 2^4.[2]
- 8.Evaluate 4^3.[2]
- 9.Simplify x^4 × x^2 ÷ x^3.[3]
- 10.Simplify x^6 × x^6 ÷ x^2.[3]
- 11.Simplify x^3 × x^5 ÷ x^4.[3]
- 12.Simplify x^6 × x^7 ÷ x^4.[3]
Show answers and working
1. 121 and 11
11² = 11 × 11 = 121 √121 = 11 because 11 × 11 = 121
2. 64 and 8
8² = 8 × 8 = 64 √64 = 8 because 8 × 8 = 64
3. 4 and 2
2² = 2 × 2 = 4 √4 = 2 because 2 × 2 = 4
4. 49 and 7
7² = 7 × 7 = 49 √49 = 7 because 7 × 7 = 49
5. 625
Multiply 5 by itself 4 times. 5 × 5 × 5 × 5 = 625
6. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
7. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
8. 64
Multiply 4 by itself 3 times. 4 × 4 × 4 = 64
9. x^3
Multiplying: add the powers → x^6. Dividing: subtract the powers → x^6 ÷ x^3 = x^3.
10. x^10
Multiplying: add the powers → x^12. Dividing: subtract the powers → x^12 ÷ x^2 = x^10.
11. x^4
Multiplying: add the powers → x^8. Dividing: subtract the powers → x^8 ÷ x^4 = x^4.
12. x^9
Multiplying: add the powers → x^13. Dividing: subtract the powers → x^13 ÷ x^4 = x^9.
Worked examples
Work out 5² and √25.
- 5² = 5 × 5 = 25
- √25 = 5 because 5 × 5 = 25
- Answer: 25 and 5
Evaluate 4^4.
- Multiply 4 by itself 4 times.
- 4 × 4 × 4 × 4 = 256
- Answer: 256
Simplify x^2 × x^3 ÷ x^3.
- Multiplying: add the powers → x^5.
- Dividing: subtract the powers → x^5 ÷ x^3 = x^2.
- Answer: x^2
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 Index Laws
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Frequently asked
- Is this Grade 3 Index Laws 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 Square Roots, Cubes, Factors and Multiples. 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 Index Laws?
- Move on to Standard Index Form, Whole Numbers, Counting, Number Recognition, which build directly on this idea.
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