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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 419 · 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 2.5 × 10⁻⁴ as a decimal. =
  2. 2.Write 5³ × 5⁴ as a single power 5ⁿ. What is n?
  3. 3.Write 6,500 in standard form as 6.5 × 10ⁿ. What is n?
  4. 4.What is the value of 3⁻³ (as a fraction)? =
  5. 5.8.8 × 10⁴ =
  6. 6.Write 6.2 × 10⁻² as a decimal. =
  7. 7.What is the value of 2² × 2⁻¹? =
  8. 8.Write 7.9 × 10⁻¹ as a decimal. =
  9. 9.8.2 × 10⁵ =
  10. 10.Write 3,20,00,000 in standard form as 3.2 × 10ⁿ. What is n?
  11. 11.What is the value of 2⁻³ (as a fraction)? =
  12. 12.What is the value of 4⁸? =
  13. 13.What is the value of 3⁴ × 3⁻⁴? =
  14. 14.Write 8¹⁶ ÷ 8⁹ as a single power 8ⁿ. What is n?
  15. 15.Write 5.4 × 10⁻⁴ as a decimal. =
  16. 16.Write 2.9 × 10⁻⁴ as a decimal. =
  17. 17.What is the value of (1/8)⁻²? =
  18. 18.What is the value of 3⁵ × 3⁻¹? =
  19. 19.1.8 × 10⁶ =
  20. 20.What is the value of 3⁻⁶ (as a fraction)? =
  21. 21.What is the value of 10¹ × 10⁻⁴? =
  22. 22.What is the value of 3² × 3⁻⁵? =
  23. 23.Write 9.2 × 10⁻¹ as a decimal. =
  24. 24.Write 8.6 × 10⁻³ as a decimal. =
  25. 25.What is the value of 10⁴? =
  26. 26.Write (4⁵)³ as a single power 4ⁿ. What is n?
  27. 27.Write 7,900 in standard form as 7.9 × 10ⁿ. What is n?
  28. 28.Write 1.3 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 2¹²? =
  30. 30.What is the value of 2¹¹? =
  31. 31.Write 8.1 × 10⁻¹ as a decimal. =
  32. 32.What is the value of 2⁷? =
  33. 33.What is the value of 5¹ × 5⁻²? =
  34. 34.Write 2.4 × 10⁻³ as a decimal. =
  35. 35.Write 4.3 × 10⁻⁴ as a decimal. =
  36. 36.Write 5.7 × 10⁻⁴ as a decimal. =
  37. 37.Write 2³ × 2³ as a single power 2ⁿ. What is n?
  38. 38.Write 2.7 × 10⁻³ as a decimal. =
  39. 39.What is the value of 4⁶? =
  40. 40.What is the value of (1/6)⁻²? =

Answer key

  1. 0.00025
  2. 7
  3. 3
  4. 1/27
  5. 88000
  6. 0.062
  7. 2
  8. 0.79
  9. 820000
  10. 7
  11. 1/8
  12. 65536
  13. 1
  14. 7
  15. 0.00054
  16. 0.00029
  17. 64
  18. 81
  19. 1800000
  20. 1/729
  21. 1/1000
  22. 1/27
  23. 0.92
  24. 0.0086
  25. 10000
  26. 15
  27. 3
  28. 0.13
  29. 4096
  30. 2048
  31. 0.81
  32. 128
  33. 1/5
  34. 0.0024
  35. 0.00043
  36. 0.00057
  37. 6
  38. 0.0027
  39. 4096
  40. 36

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