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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 19 · 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 56,000 in standard form as 5.6 × 10ⁿ. What is n?
  2. 2.What is the value of (1/4)⁻²? =
  3. 3.Write 8.1 × 10⁻¹ as a decimal. =
  4. 4.What is the value of 3⁷? =
  5. 5.Write 5⁷ × 5² as a single power 5ⁿ. What is n?
  6. 6.What is the value of 10³? =
  7. 7.What is the value of 10⁴? =
  8. 8.What is the value of 10¹ × 10⁻²? =
  9. 9.What is the value of 9²? =
  10. 10.Write 2⁴ × 2⁴ as a single power 2ⁿ. What is n?
  11. 11.What is the value of 4⁻² (as a fraction)? =
  12. 12.What is the value of (6/7)⁻²? =
  13. 13.What is the value of 2⁻⁸ (as a fraction)? =
  14. 14.Write 42,00,000 in standard form as 4.2 × 10ⁿ. What is n?
  15. 15.What is the value of 2⁴ × 2⁻⁴? =
  16. 16.What is the value of 6⁵? =
  17. 17.What is the value of (1/3)⁻¹? =
  18. 18.Write 6.9 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 7⁻³ (as a fraction)? =
  20. 20.Write (8⁷)⁶ as a single power 8ⁿ. What is n?
  21. 21.Write (3³)⁶ as a single power 3ⁿ. What is n?
  22. 22.Write (2⁹)⁸ as a single power 2ⁿ. What is n?
  23. 23.Write 3.4 × 10⁻¹ as a decimal. =
  24. 24.8.4 × 10³ =
  25. 25.Write 2¹¹ ÷ 2⁸ as a single power 2ⁿ. What is n?
  26. 26.Write 4.7 × 10⁻¹ as a decimal. =
  27. 27.What is the value of 2⁻⁹ (as a fraction)? =
  28. 28.Write 2.1 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 3⁹? =
  30. 30.What is the value of (4/9)⁻²? =
  31. 31.What is the value of 3³ × 3⁻⁵? =
  32. 32.7.3 × 10³ =
  33. 33.Write (2⁷)⁷ as a single power 2ⁿ. What is n?
  34. 34.Write 7.7 × 10⁻³ as a decimal. =
  35. 35.Write (5⁴)³ as a single power 5ⁿ. What is n?
  36. 36.What is the value of 9⁻³ (as a fraction)? =
  37. 37.Write 510 in standard form as 5.1 × 10ⁿ. What is n?
  38. 38.4.9 × 10³ =
  39. 39.What is the value of 2⁵ × 2⁻⁶? =
  40. 40.Write 8.8 × 10⁻² as a decimal. =

Answer key

  1. 4
  2. 16
  3. 0.81
  4. 2187
  5. 9
  6. 1000
  7. 10000
  8. 1/10
  9. 81
  10. 8
  11. 1/16
  12. 49/36
  13. 1/256
  14. 6
  15. 1
  16. 7776
  17. 3
  18. 0.00069
  19. 1/343
  20. 42
  21. 18
  22. 72
  23. 0.34
  24. 8400
  25. 3
  26. 0.47
  27. 1/512
  28. 0.21
  29. 19683
  30. 81/16
  31. 1/9
  32. 7300
  33. 49
  34. 0.0077
  35. 12
  36. 1/729
  37. 2
  38. 4900
  39. 1/2
  40. 0.088

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