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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 33 · 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 7¹⁵ ÷ 7⁹ as a single power 7ⁿ. What is n?
  2. 2.What is the value of 3²? =
  3. 3.What is the value of (1/3)⁻²? =
  4. 4.Write 7² × 7⁴ as a single power 7ⁿ. What is n?
  5. 5.What is the value of 3⁻³ (as a fraction)? =
  6. 6.Write 5.9 × 10⁻¹ as a decimal. =
  7. 7.What is the value of 7⁵? =
  8. 8.What is the value of 5⁷? =
  9. 9.2.1 × 10³ =
  10. 10.What is the value of 4⁻⁴ (as a fraction)? =
  11. 11.What is the value of 2³ × 2⁻³? =
  12. 12.Write 6⁵ × 6⁹ as a single power 6ⁿ. What is n?
  13. 13.Write (4⁷)⁸ as a single power 4ⁿ. What is n?
  14. 14.Write 5.1 × 10⁻³ as a decimal. =
  15. 15.Write 5.7 × 10⁻³ as a decimal. =
  16. 16.What is the value of 4⁻² (as a fraction)? =
  17. 17.Write 5.2 × 10⁻² as a decimal. =
  18. 18.What is the value of 4³? =
  19. 19.Write 770 in standard form as 7.7 × 10ⁿ. What is n?
  20. 20.What is the value of 6⁻³ (as a fraction)? =
  21. 21.What is the value of 3¹ × 3⁻⁶? =
  22. 22.Write 9² × 9⁸ as a single power 9ⁿ. What is n?
  23. 23.2.6 × 10⁷ =
  24. 24.What is the value of 3³ × 3⁻⁵? =
  25. 25.What is the value of 2⁸? =
  26. 26.What is the value of 10⁵ × 10⁻⁵? =
  27. 27.What is the value of 2³? =
  28. 28.Write 9.1 × 10⁻⁴ as a decimal. =
  29. 29.What is the value of 2⁻⁶ (as a fraction)? =
  30. 30.Write 6.4 × 10⁻¹ as a decimal. =
  31. 31.Write 9.8 × 10⁻¹ as a decimal. =
  32. 32.What is the value of (2/5)⁻¹? =
  33. 33.Write 2.2 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 5⁴ × 5⁻⁵? =
  35. 35.What is the value of 4⁸? =
  36. 36.What is the value of 2¹²? =
  37. 37.What is the value of 3³ × 3⁻⁶? =
  38. 38.Write 7⁶ ÷ 7⁴ as a single power 7ⁿ. What is n?
  39. 39.Write 2,70,000 in standard form as 2.7 × 10ⁿ. What is n?
  40. 40.Write 3.5 × 10⁻¹ as a decimal. =

Answer key

  1. 6
  2. 9
  3. 9
  4. 6
  5. 1/27
  6. 0.59
  7. 16807
  8. 78125
  9. 2100
  10. 1/256
  11. 1
  12. 14
  13. 56
  14. 0.0051
  15. 0.0057
  16. 1/16
  17. 0.052
  18. 64
  19. 2
  20. 1/216
  21. 1/243
  22. 10
  23. 26000000
  24. 1/9
  25. 256
  26. 1
  27. 8
  28. 0.00091
  29. 1/64
  30. 0.64
  31. 0.98
  32. 5/2
  33. 0.22
  34. 1/5
  35. 65536
  36. 4096
  37. 1/27
  38. 2
  39. 5
  40. 0.35

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