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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 271 · 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 2,800 in standard form as 2.8 × 10ⁿ. What is n?
  2. 2.Write 9.4 × 10⁻⁴ as a decimal. =
  3. 3.What is the value of 2⁻⁴ (as a fraction)? =
  4. 4.What is the value of 6⁻² (as a fraction)? =
  5. 5.What is the value of 10⁵? =
  6. 6.What is the value of (6/7)⁻²? =
  7. 7.Write 6,70,000 in standard form as 6.7 × 10ⁿ. What is n?
  8. 8.Write 5.8 × 10⁻³ as a decimal. =
  9. 9.What is the value of 5⁶ × 5⁻³? =
  10. 10.What is the value of 2¹³? =
  11. 11.1.9 × 10² =
  12. 12.Write 3.5 × 10⁻² as a decimal. =
  13. 13.What is the value of (2/5)⁻²? =
  14. 14.Write 850 in standard form as 8.5 × 10ⁿ. What is n?
  15. 15.5.2 × 10⁷ =
  16. 16.What is the value of 3³ × 3⁻³? =
  17. 17.What is the value of (4/5)⁻¹? =
  18. 18.Write (4⁸)⁴ as a single power 4ⁿ. What is n?
  19. 19.What is the value of 9³? =
  20. 20.What is the value of 5⁻¹ (as a fraction)? =
  21. 21.What is the value of 3¹ × 3⁻⁶? =
  22. 22.Write 4⁹ × 4⁹ as a single power 4ⁿ. What is n?
  23. 23.What is the value of (4/9)⁻¹? =
  24. 24.What is the value of 4⁸? =
  25. 25.Write 5.6 × 10⁻⁴ as a decimal. =
  26. 26.Write 9.7 × 10⁻³ as a decimal. =
  27. 27.What is the value of 5⁵ × 5⁻³? =
  28. 28.Write 9.2 × 10⁻² as a decimal. =
  29. 29.What is the value of 7⁴? =
  30. 30.Write 9¹³ ÷ 9⁵ as a single power 9ⁿ. What is n?
  31. 31.Write (9³)⁸ as a single power 9ⁿ. What is n?
  32. 32.What is the value of (1/3)⁻²? =
  33. 33.What is the value of 5⁵ × 5⁻²? =
  34. 34.What is the value of (7/9)⁻²? =
  35. 35.What is the value of 5⁴? =
  36. 36.Write 940 in standard form as 9.4 × 10ⁿ. What is n?
  37. 37.Write 5,20,00,000 in standard form as 5.2 × 10ⁿ. What is n?
  38. 38.Write 4.1 × 10⁻¹ as a decimal. =
  39. 39.What is the value of 5⁵ × 5⁻⁵? =
  40. 40.What is the value of 2¹¹? =

Answer key

  1. 3
  2. 0.00094
  3. 1/16
  4. 1/36
  5. 100000
  6. 49/36
  7. 5
  8. 0.0058
  9. 125
  10. 8192
  11. 190
  12. 0.035
  13. 25/4
  14. 2
  15. 52000000
  16. 1
  17. 5/4
  18. 32
  19. 729
  20. 1/5
  21. 1/243
  22. 18
  23. 9/4
  24. 65536
  25. 0.00056
  26. 0.0097
  27. 25
  28. 0.092
  29. 2401
  30. 8
  31. 24
  32. 9
  33. 125
  34. 81/49
  35. 625
  36. 2
  37. 7
  38. 0.41
  39. 1
  40. 2048

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