Exponents practice
Free exponents practice: pick a skill and answer 10 questions, marked as you go, with the working shown when an answer is wrong.
🧒 Kids: pick a skill, work it out and tap Check ✓! Remember, 2³ means 2 × 2 × 2, not 2 × 3.
Ready-made practice rounds: 15 skills by grade
| Skill | What your child does | Grade |
|---|---|---|
| Write as a power | 5 × 5 × 5 = 5³: find the base and the exponent. | 6 |
| Work out powers | 2⁵, 3⁴ and 10³ step by step. | 6 |
| Square numbers | 12² and “what number squared makes 81?” | 5–6 |
| Cube numbers | 4³ and “what number cubed makes 125?” | 6 |
| Powers of 10 | 10⁴ = 10,000 and 7 × 10³. | 5 |
| Square roots | √144 and √25 + √9. | 6–8 |
| Cube roots | ∛64 and ∛(−27). | 8 |
| Estimate square roots | √50 is between 7 and 8. | 8 |
| Product and quotient rules | 2⁴ × 2⁵ = 2⁹ and 5⁷ ÷ 5³ = 5⁴. | 8 |
| Power rules | (3²)⁴ = 3⁸ and (2 × 5)². | 8 |
| Zero and negative exponents | 7⁰ = 1, 2⁻³ = 1/8 and 10⁻² = 0.01. | 8 |
| Negative bases | (−2)³ = −8, but −3² = −9. | 7–8 |
| Scientific notation | 45,000 = 4.5 × 10⁴ and back again. | 8 |
| Multiply and divide in scientific notation | (3 × 10⁴) × (2 × 10⁵). | 8 |
| True or false | Is 2³ = 6? Is 3² × 3³ = 3⁵? | 6–8 |
Each link opens the practice tool on that skill, so you can bookmark or share the one your child needs.
How to use the exponents practice
- Pick a skill. If you are not sure, start with “write as a power” and move down the table as each one gets easy.
- Work it out on paper. Writing 3⁴ as 3 × 3 × 3 × 3 first stops most mistakes.
- Type the answer. Some questions have two boxes, like the base and the exponent, or the top and bottom of a fraction. On a phone, a number pad appears below.
- Read the working when an answer is wrong. The hint shows each multiplication, or the rule used.
- Check the stars. 8 or more out of 10 means the skill is secure. The results list the questions to practice again.
The idea in one line
An exponent says how many times to use the base as a factor. So 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The small number is the exponent, and the big number is the base.
The mistake children make most is multiplying the base by the exponent. 2⁵ is not 10, and 3² is not 6. Saying “three times three” out loud for 3² helps it stick.
How answers are marked
- Whole numbers are marked by value, with or without commas.
- Fractions have a top box and a bottom box. 2⁻² can be typed as 1/4, and an equal fraction like 2/8 for 2⁻³ also counts.
- Decimals like 0.01 for 10⁻² can be typed with or without the 0 in front.
- Scientific notation has one box for the number between 1 and 10 and one for the power of 10.
- True or false and “which power is the same?” use big buttons instead of a box.
A sensible order for practice
Exponents build over four years. This order follows the US Common Core and the NCERT books:
- Powers of 10 (grade 5, 5.NBT.A.2): 10³ = 1,000, and multiplying by powers of 10.
- Write and work out powers (grade 6, 6.EE.A.1): 5³ = 5 × 5 × 5 = 125, squares and cubes.
- Square and cube roots (grades 6 to 8, 8.EE.A.2): roots undo squares and cubes. Estimating roots like √50 comes in grade 8 (8.NS.A.2).
- The exponent rules (grade 8, 8.EE.A.1): add, subtract or multiply the exponents. The exponent calculator shows why each rule works.
- Zero and negative exponents, then scientific notation (grade 8, 8.EE.A.3 and 8.EE.A.4).
When a skill won’t stick
- Multiplying base × exponent: ask your child to write the power out in full, 4³ = 4 × 4 × 4, before working it out.
- Mixing up squares and square roots: squaring makes a number bigger (6² = 36), and the square root goes back (√36 = 6). Draw the square.
- Adding exponents when the bases differ: 2³ × 3² can’t be simplified with a rule. The rules only work for the same base.
- Thinking a negative exponent makes a negative number: 2⁻³ = 1/8, a small positive number. The pattern table in the calculator shows why.
- Losing the brackets: (−3)² = 9, but −3² = −9, because the power belongs only to the 3.
A 10-minute routine
- Minutes 1–2: say the squares from 1² to 12² out loud, like times tables.
- Minutes 3–8: one round of 10 questions on the current skill.
- Minutes 9–10: check one hard question in the calculator and compare the working.
Exponents by grade
| Grade | What children practice | Standard |
|---|---|---|
| Grade 5 | Powers of 10 and multiplying by them | 5.NBT.A.2 |
| Grade 6 | Writing and working out whole-number exponents | 6.EE.A.1 |
| Grade 8 | Exponent rules, zero and negative exponents | 8.EE.A.1 |
| Grade 8 | Square and cube roots, estimating roots | 8.EE.A.2, 8.NS.A.2 |
| Grade 8 | Scientific notation and its operations | 8.EE.A.3, 8.EE.A.4 |
In India, the class 8 chapters “A Square and a Cube” and “Power Play” cover squares, roots and exponents.
For parents and teachers in the classroom
- Share a skill: add ?skill=write, eval, sq, cube, p10, sqrt, cbrt, est, prod, pow, zero, negb, sci, sops or tf to the address.
- Projector friendly: large numbers and big answer buttons work well for a whole-class warm-up.
- Private by design: no account and nothing stored online.
More exponents help
- Exponents practice: 10 questions on any of 15 skills, marked as you go.
- Exponent calculator: any base and exponent, with every step and the pattern table.
- Order of operations with exponents: why 2 × 3² is 18, not 36.
- Multiplying integers: why (−3)² is 9 but −3² is −9.
- Multiplying by 10, 100 and 1,000: the start of powers of 10.
- Worksheets: exponents worksheet · exponent rules · scientific notation · square roots · make a fresh test
Back to exponents for kids · 6th grade math · 8th grade math
Last reviewed
Questions parents ask
How can my child practice exponents online for free?
Use the practice tool at the top of this page. Pick a skill, such as square numbers or exponent rules, and answer 10 questions one at a time. Every answer is marked straight away, and a wrong answer shows the working.
Which exponents skill should my child start with?
Start with writing a multiplication as a power and working out small powers like 2⁵. Then do square numbers, cube numbers and powers of 10 before moving on to roots and the exponent rules.
What grade learns exponents?
Grade 5 meets powers of 10 (5.NBT.A.2). Grade 6 writes and works out whole-number exponents (6.EE.A.1). Grade 8 learns the exponent rules, square and cube roots and scientific notation (8.EE.A.1 to 8.EE.A.4).
How do I type a fraction or a negative answer?
Fractions have a box for the top and a box for the bottom, so 2⁻³ is 1 on top and 8 on the bottom. Use the minus key for negative answers, like (−2)³ = −8.
How are scientific notation answers marked?
There is one box for the number between 1 and 10 and one for the power of 10. For 45,000, type 4.5 and 4. A negative power, like 10⁻³, uses the minus key.
Can teachers link to one skill?
Yes. Add ?skill= to the address, for example /exponents/practice/?skill=sqrt for square roots. Every child gets their own random questions, and nothing needs a login.