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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 729 · 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 2.4 × 10⁻⁴ as a decimal. =
  2. 2.What is the value of (3/7)⁻¹? =
  3. 3.Write 6.1 × 10⁻³ as a decimal. =
  4. 4.What is the value of 4⁻³ (as a fraction)? =
  5. 5.What is the value of 2³ × 2⁻⁴? =
  6. 6.Write 2,500 in standard form as 2.5 × 10ⁿ. What is n?
  7. 7.Write 6,80,000 in standard form as 6.8 × 10ⁿ. What is n?
  8. 8.What is the value of 6⁵? =
  9. 9.4.5 × 10⁷ =
  10. 10.What is the value of 3⁶ × 3⁻⁴? =
  11. 11.What is the value of 3² × 3⁻¹? =
  12. 12.Write 7.6 × 10⁻⁴ as a decimal. =
  13. 13.Write (5⁷)⁷ as a single power 5ⁿ. What is n?
  14. 14.1.6 × 10⁶ =
  15. 15.What is the value of 3⁶ × 3⁻²? =
  16. 16.What is the value of (3/8)⁻²? =
  17. 17.What is the value of 6⁻² (as a fraction)? =
  18. 18.Write 4⁴ × 4⁶ as a single power 4ⁿ. What is n?
  19. 19.What is the value of (1/5)⁻¹? =
  20. 20.What is the value of 5² × 5⁻⁴? =
  21. 21.What is the value of 5²? =
  22. 22.What is the value of 3⁵ × 3⁻⁶? =
  23. 23.Write 4.1 × 10⁻⁴ as a decimal. =
  24. 24.Write 5⁷ × 5⁸ as a single power 5ⁿ. What is n?
  25. 25.Write 9¹⁶ ÷ 9⁷ as a single power 9ⁿ. What is n?
  26. 26.What is the value of 5⁶ × 5⁻³? =
  27. 27.Write 1.9 × 10⁻³ as a decimal. =
  28. 28.Write 5⁸ ÷ 5⁵ as a single power 5ⁿ. What is n?
  29. 29.Write 81,000 in standard form as 8.1 × 10ⁿ. What is n?
  30. 30.Write 3² × 3² as a single power 3ⁿ. What is n?
  31. 31.Write 3.3 × 10⁻⁴ as a decimal. =
  32. 32.Write (8⁴)⁵ as a single power 8ⁿ. What is n?
  33. 33.Write 9⁹ ÷ 9⁴ as a single power 9ⁿ. What is n?
  34. 34.What is the value of (8/9)⁻¹? =
  35. 35.What is the value of 8²? =
  36. 36.What is the value of 10³ × 10⁻²? =
  37. 37.What is the value of 7²? =
  38. 38.Write 8.7 × 10⁻³ as a decimal. =
  39. 39.What is the value of 2⁸? =
  40. 40.What is the value of (4/5)⁻²? =

Answer key

  1. 0.00024
  2. 7/3
  3. 0.0061
  4. 1/64
  5. 1/2
  6. 3
  7. 5
  8. 7776
  9. 45000000
  10. 9
  11. 3
  12. 0.00076
  13. 49
  14. 1600000
  15. 81
  16. 64/9
  17. 1/36
  18. 10
  19. 5
  20. 1/25
  21. 25
  22. 1/3
  23. 0.00041
  24. 15
  25. 9
  26. 125
  27. 0.0019
  28. 3
  29. 4
  30. 4
  31. 0.00033
  32. 20
  33. 5
  34. 9/8
  35. 64
  36. 10
  37. 49
  38. 0.0087
  39. 256
  40. 25/16

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