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Grade 1–3Common Core (CCSS) · Math: number sense

Exponents, Square Roots and Standard Form — Worksheets

Practise powers, exponent rules, square roots and standard form with new numbers every time.

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Powers, square roots and standard form · 14-16 years

Name: ____________________

Worked example

  1. The goal: work out the value of a power (e.g. 2³) or a root (e.g. √49).
  2. Power: 2³ means 2 × 2 × 2 = 8. The exponent tells how many times the base is multiplied by itself.
  3. Square root: √25 = 5, because 5 × 5 = 25.
  4. Scientific notation: 4,500 = 4.5 × 10³ – a number between 1 and 10 times a power of ten.
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓
Example: how to solve it
1.

Calculate: x² · x⁴ =

2.

Calculate: 3⁶ / 3⁵ =

3.

Calculate: 3⁴ =

4.

Calculate: 10² =

5.

Calculate: 2⁴ · 2⁴ =

6.

Write in standard form: 480,000

7.

Calculate: 5² · 5³ =

8.

Calculate: √16 =

9.

Write in standard form: 5400

10.

Write in standard form: 59,000

11.

Calculate: 8² =

12.

Write as an ordinary number: 9.3 · 10³

13.

Write in standard form: 4,400,000

14.

Calculate: a⁶ / a³ =

15.

Write in standard form: 83,000

16.

Write in standard form: 150,000

17.

Calculate: 5⁶ · 5³ =

18.

Calculate: 2³ · 2⁶ =

19.

Write as an ordinary number: 9.3 · 10⁵

20.

Write as an ordinary number: 2.7 · 10⁶

Answer key

  1. 1. x⁶
  2. 2. 3¹
  3. 3. 81
  4. 4. 100
  5. 5. 2⁸
  6. 6. 4.8 · 10⁵
  7. 7. 5⁵
  8. 8. 4
  9. 9. 5.4 · 10³
  10. 10. 5.9 · 10⁴
  11. 11. 64
  12. 12. 9300
  13. 13. 4.4 · 10⁶
  14. 14. a³
  15. 15. 8.3 · 10⁴
  16. 16. 1.5 · 10⁵
  17. 17. 5⁹
  18. 18. 2⁹
  19. 19. 930,000
  20. 20. 2,700,000

Created with WorksheetMint

Topics on this worksheet

Areas on this sheet

  • Number sense · 20

Step 1 of 5

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Your choices

Area
Algebra
Exercise type
Powers, square roots and standard form
Age
14–16 years
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
1. Choose content
Area
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How to use the tool

  1. Choose the exercise type powers, square roots and standard form.
  2. Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
  3. Print or save as PDF. “Create new version” gives new numbers with a matching answer key.

About this generator

Powers make big and small numbers manageable. The sheets cover calculating powers, the rules aᵐ · aⁿ = aᵐ⁺ⁿ and aᵐ / aⁿ = aᵐ⁻ⁿ, square roots of perfect squares and writing numbers in standard form. For algebra, the generator also offers the square rules, the conjugate rule and factorising. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.

Popular uses

  • Exponent rules
  • Scientific notation in science lessons
  • Square rules and factorising
  • Revision before a test

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Frequently asked questions

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
What is standard form?
A number written as a · 10ⁿ with 1 ≤ a < 10, for example 45 000 = 4.5 · 10⁴.
What is aᵐ · aⁿ?
Add the exponents: aᵐ⁺ⁿ.

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