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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 223 · 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 3.3 × 10⁻³ as a decimal. =
  2. 2.Write 9.5 × 10⁻¹ as a decimal. =
  3. 3.What is the value of (5/8)⁻²? =
  4. 4.What is the value of 2⁷? =
  5. 5.7.2 × 10⁶ =
  6. 6.Write 9.2 × 10⁻⁴ as a decimal. =
  7. 7.Write 8⁷ ÷ 8⁴ as a single power 8ⁿ. What is n?
  8. 8.What is the value of 10³ × 10⁻⁴? =
  9. 9.What is the value of 10⁵ × 10⁻⁶? =
  10. 10.What is the value of 4⁻³ (as a fraction)? =
  11. 11.What is the value of 10⁶ × 10⁻¹? =
  12. 12.3.5 × 10⁷ =
  13. 13.What is the value of (2/7)⁻²? =
  14. 14.Write 6.8 × 10⁻¹ as a decimal. =
  15. 15.What is the value of 10²? =
  16. 16.What is the value of (1/3)⁻¹? =
  17. 17.Write (4⁴)⁹ as a single power 4ⁿ. What is n?
  18. 18.What is the value of 6³? =
  19. 19.Write 6¹³ ÷ 6⁹ as a single power 6ⁿ. What is n?
  20. 20.Write 9⁷ ÷ 9² as a single power 9ⁿ. What is n?
  21. 21.Write 4⁴ × 4³ as a single power 4ⁿ. What is n?
  22. 22.Write (3⁹)⁵ as a single power 3ⁿ. What is n?
  23. 23.Write 9.5 × 10⁻² as a decimal. =
  24. 24.What is the value of 2⁴ × 2⁻⁶? =
  25. 25.4.9 × 10⁵ =
  26. 26.Write 3⁷ × 3⁷ as a single power 3ⁿ. What is n?
  27. 27.What is the value of 7⁻¹ (as a fraction)? =
  28. 28.Write 3.5 × 10⁻⁴ as a decimal. =
  29. 29.What is the value of 4⁸? =
  30. 30.What is the value of 9²? =
  31. 31.Write 3.7 × 10⁻⁴ as a decimal. =
  32. 32.What is the value of 3⁻⁴ (as a fraction)? =
  33. 33.Write 970 in standard form as 9.7 × 10ⁿ. What is n?
  34. 34.3.7 × 10⁴ =
  35. 35.What is the value of 2⁹? =
  36. 36.Write (8⁹)³ as a single power 8ⁿ. What is n?
  37. 37.Write 4.8 × 10⁻¹ as a decimal. =
  38. 38.What is the value of 3⁴ × 3⁻⁶? =
  39. 39.Write (2⁴)² as a single power 2ⁿ. What is n?
  40. 40.Write 7 × 10⁻⁴ as a decimal. =

Answer key

  1. 0.0033
  2. 0.95
  3. 64/25
  4. 128
  5. 7200000
  6. 0.00092
  7. 3
  8. 1/10
  9. 1/10
  10. 1/64
  11. 100000
  12. 35000000
  13. 49/4
  14. 0.68
  15. 100
  16. 3
  17. 36
  18. 216
  19. 4
  20. 5
  21. 7
  22. 45
  23. 0.095
  24. 1/4
  25. 490000
  26. 14
  27. 1/7
  28. 0.00035
  29. 65536
  30. 81
  31. 0.00037
  32. 1/81
  33. 2
  34. 37000
  35. 512
  36. 27
  37. 0.48
  38. 1/9
  39. 8
  40. 0.0007

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