Free Grade 3 Standard Index Form Lessons
Free Grade 3 lessons for Standard Index Form: 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain standard index form
Explain standard index form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate standard index form
Calculate standard index form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare standard index form
Compare standard index form accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify standard index form
Justify standard index form 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 Standard Index Form 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 12² and √144.[1]
- 3.Work out 6² and √36.[1]
- 4.Work out 10² and √100.[1]
- 5.Evaluate 3^4.[2]
- 6.Evaluate 5^4.[2]
- 7.Evaluate 2^3.[2]
- 8.Evaluate 2^4.[2]
- 9.Simplify x^6 × x^7 ÷ x^2.[3]
- 10.Simplify x^4 × x^6 ÷ x^4.[3]
- 11.Simplify x^3 × x^4 ÷ x^4.[3]
- 12.Simplify x^2 × x^7 ÷ x^2.[3]
Show answers and working
1. 49 and 7
7² = 7 × 7 = 49 √49 = 7 because 7 × 7 = 49
2. 144 and 12
12² = 12 × 12 = 144 √144 = 12 because 12 × 12 = 144
3. 36 and 6
6² = 6 × 6 = 36 √36 = 6 because 6 × 6 = 36
4. 100 and 10
10² = 10 × 10 = 100 √100 = 10 because 10 × 10 = 100
5. 81
Multiply 3 by itself 4 times. 3 × 3 × 3 × 3 = 81
6. 625
Multiply 5 by itself 4 times. 5 × 5 × 5 × 5 = 625
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^11
Multiplying: add the powers → x^13. Dividing: subtract the powers → x^13 ÷ x^2 = x^11.
10. x^6
Multiplying: add the powers → x^10. Dividing: subtract the powers → x^10 ÷ x^4 = x^6.
11. x^3
Multiplying: add the powers → x^7. Dividing: subtract the powers → x^7 ÷ x^4 = x^3.
12. x^7
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^2 = x^7.
Worked examples
Work out 9² and √81.
- 9² = 9 × 9 = 81
- √81 = 9 because 9 × 9 = 81
- Answer: 81 and 9
Evaluate 4^3.
- Multiply 4 by itself 3 times.
- 4 × 4 × 4 = 64
- Answer: 64
Simplify x^3 × x^7 ÷ x^2.
- Multiplying: add the powers → x^10.
- Dividing: subtract the powers → x^10 ÷ x^2 = x^8.
- Answer: x^8
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 Standard Index Form
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Standard Index Form lesson really free?
- Yes. Every lessons 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 Index Laws, Square Roots, Factors and Multiples. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Standard Index Form?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
Related resources
Stuck on Standard Index Form? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor