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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 700 · 40 sums
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The method (Same base, work the powers): aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1. a⁻ⁿ = 1/aⁿ, and (a/b)⁻ⁿ = (b/a)ⁿ. Standard form: one digit before the point × a power of 10 — 4500000 = 4.5 × 10⁶. × 10⁻ⁿ moves the decimal point n places to the left: 2.5 × 10⁻³ = 0.0025.

NameDateTime takenScore ___ / 40
  1. 1.Write 8³ × 8³ as a single power 8ⁿ. What is n?
  2. 2.Write 2.5 × 10⁻³ as a decimal. =
  3. 3.Write 71,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  4. 4.What is the value of 7²? =
  5. 5.What is the value of (2/7)⁻¹? =
  6. 6.Write (9³)⁸ as a single power 9ⁿ. What is n?
  7. 7.Write (3⁴)⁴ as a single power 3ⁿ. What is n?
  8. 8.What is the value of 10²? =
  9. 9.Write 3 × 10⁻⁴ as a decimal. =
  10. 10.What is the value of 3⁴? =
  11. 11.What is the value of 7⁻¹ (as a fraction)? =
  12. 12.Write 8.7 × 10⁻³ as a decimal. =
  13. 13.What is the value of 10⁴? =
  14. 14.What is the value of 5⁴ × 5⁻¹? =
  15. 15.What is the value of 6⁻¹ (as a fraction)? =
  16. 16.What is the value of 3⁴ × 3⁻⁶? =
  17. 17.Write 55,00,000 in standard form as 5.5 × 10ⁿ. What is n?
  18. 18.Write 6 × 10⁻¹ as a decimal. =
  19. 19.What is the value of (3/4)⁻¹? =
  20. 20.Write 4,600 in standard form as 4.6 × 10ⁿ. What is n?
  21. 21.What is the value of 3³? =
  22. 22.What is the value of (1/6)⁻¹? =
  23. 23.Write 9² × 9³ as a single power 9ⁿ. What is n?
  24. 24.Write 1.8 × 10⁻² as a decimal. =
  25. 25.What is the value of 5³ × 5⁻¹? =
  26. 26.What is the value of 5⁻³ (as a fraction)? =
  27. 27.What is the value of 9⁴? =
  28. 28.Write 8.4 × 10⁻⁴ as a decimal. =
  29. 29.Write 2⁶ × 2⁹ as a single power 2ⁿ. What is n?
  30. 30.Write 1.8 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 2²? =
  32. 32.Write 4.1 × 10⁻² as a decimal. =
  33. 33.What is the value of 5⁻⁴ (as a fraction)? =
  34. 34.2.2 × 10³ =
  35. 35.What is the value of (3/5)⁻²? =
  36. 36.What is the value of 5² × 5⁻¹? =
  37. 37.Write 1.8 × 10⁻¹ as a decimal. =
  38. 38.What is the value of 8⁵? =
  39. 39.What is the value of 9⁻² (as a fraction)? =
  40. 40.Write 670 in standard form as 6.7 × 10ⁿ. What is n?

Answer key

  1. 6
  2. 0.0025
  3. 6
  4. 49
  5. 7/2
  6. 24
  7. 16
  8. 100
  9. 0.0003
  10. 81
  11. 1/7
  12. 0.0087
  13. 10000
  14. 125
  15. 1/6
  16. 1/9
  17. 6
  18. 0.6
  19. 4/3
  20. 3
  21. 27
  22. 6
  23. 5
  24. 0.018
  25. 25
  26. 1/125
  27. 6561
  28. 0.00084
  29. 15
  30. 0.00018
  31. 4
  32. 0.041
  33. 1/625
  34. 2200
  35. 25/9
  36. 5
  37. 0.18
  38. 32768
  39. 1/81
  40. 2

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