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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 418 · 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.What is the value of 5⁴? =
  2. 2.What is the value of 3³? =
  3. 3.Write 3⁹ ÷ 3⁴ as a single power 3ⁿ. What is n?
  4. 4.Write 6.5 × 10⁻¹ as a decimal. =
  5. 5.7.4 × 10⁵ =
  6. 6.Write 2.1 × 10⁻¹ as a decimal. =
  7. 7.7.1 × 10⁵ =
  8. 8.Write 35,00,000 in standard form as 3.5 × 10ⁿ. What is n?
  9. 9.Write 36,00,000 in standard form as 3.6 × 10ⁿ. What is n?
  10. 10.Write 3³ × 3⁸ as a single power 3ⁿ. What is n?
  11. 11.What is the value of 3⁷? =
  12. 12.Write 8.9 × 10⁻⁴ as a decimal. =
  13. 13.What is the value of 5² × 5⁻⁵? =
  14. 14.What is the value of 2¹³? =
  15. 15.What is the value of 5⁶ × 5⁻¹? =
  16. 16.What is the value of 8³? =
  17. 17.What is the value of (3/5)⁻¹? =
  18. 18.Write 3⁹ × 3⁵ as a single power 3ⁿ. What is n?
  19. 19.Write 6⁷ × 6⁹ as a single power 6ⁿ. What is n?
  20. 20.What is the value of (3/4)⁻¹? =
  21. 21.What is the value of 5¹ × 5⁻⁶? =
  22. 22.What is the value of 6⁴? =
  23. 23.Write 8.8 × 10⁻⁴ as a decimal. =
  24. 24.Write 60,000 in standard form as 6 × 10ⁿ. What is n?
  25. 25.3.5 × 10⁷ =
  26. 26.What is the value of 3² × 3⁻⁵? =
  27. 27.What is the value of 5⁶ × 5⁻²? =
  28. 28.Write 2,100 in standard form as 2.1 × 10ⁿ. What is n?
  29. 29.What is the value of 3¹ × 3⁻⁶? =
  30. 30.What is the value of 4⁻⁴ (as a fraction)? =
  31. 31.Write 1.7 × 10⁻⁴ as a decimal. =
  32. 32.What is the value of 10³ × 10⁻²? =
  33. 33.Write 1.3 × 10⁻³ as a decimal. =
  34. 34.Write (3⁷)⁵ as a single power 3ⁿ. What is n?
  35. 35.Write 5 × 10⁻⁴ as a decimal. =
  36. 36.Write 6.2 × 10⁻² as a decimal. =
  37. 37.What is the value of 2¹ × 2⁻⁶? =
  38. 38.What is the value of 9³? =
  39. 39.What is the value of 2⁵ × 2⁻¹? =
  40. 40.What is the value of 5³ × 5⁻³? =

Answer key

  1. 625
  2. 27
  3. 5
  4. 0.65
  5. 740000
  6. 0.21
  7. 710000
  8. 6
  9. 6
  10. 11
  11. 2187
  12. 0.00089
  13. 1/125
  14. 8192
  15. 3125
  16. 512
  17. 5/3
  18. 14
  19. 16
  20. 4/3
  21. 1/3125
  22. 1296
  23. 0.00088
  24. 4
  25. 35000000
  26. 1/27
  27. 625
  28. 3
  29. 1/243
  30. 1/256
  31. 0.00017
  32. 10
  33. 0.0013
  34. 35
  35. 0.0005
  36. 0.062
  37. 1/32
  38. 729
  39. 16
  40. 1

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