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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 414 · 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 (3⁶)⁵ as a single power 3ⁿ. What is n?
  2. 2.Write 5.5 × 10⁻² as a decimal. =
  3. 3.What is the value of 5⁴ × 5⁻¹? =
  4. 4.What is the value of 3⁴? =
  5. 5.Write (5⁷)⁵ as a single power 5ⁿ. What is n?
  6. 6.What is the value of (3/5)⁻¹? =
  7. 7.Write 7¹⁰ ÷ 7² as a single power 7ⁿ. What is n?
  8. 8.Write 730 in standard form as 7.3 × 10ⁿ. What is n?
  9. 9.Write (6⁴)³ as a single power 6ⁿ. What is n?
  10. 10.6.6 × 10⁶ =
  11. 11.Write 2 × 10⁻⁴ as a decimal. =
  12. 12.What is the value of 3⁴ × 3⁻⁴? =
  13. 13.6.3 × 10⁷ =
  14. 14.What is the value of 2⁹? =
  15. 15.Write (8⁵)³ as a single power 8ⁿ. What is n?
  16. 16.3.4 × 10⁶ =
  17. 17.What is the value of (5/6)⁻²? =
  18. 18.Write 41,00,000 in standard form as 4.1 × 10ⁿ. What is n?
  19. 19.Write 5.7 × 10⁻¹ as a decimal. =
  20. 20.What is the value of 9⁻² (as a fraction)? =
  21. 21.What is the value of 2⁶ × 2⁻⁵? =
  22. 22.Write 2.7 × 10⁻² as a decimal. =
  23. 23.What is the value of 7²? =
  24. 24.What is the value of 5³? =
  25. 25.What is the value of 2³ × 2⁻⁶? =
  26. 26.What is the value of (1/9)⁻²? =
  27. 27.What is the value of 2¹³? =
  28. 28.Write 8.5 × 10⁻³ as a decimal. =
  29. 29.Write 9⁵ × 9⁹ as a single power 9ⁿ. What is n?
  30. 30.4.2 × 10³ =
  31. 31.What is the value of 7⁻³ (as a fraction)? =
  32. 32.Write 9.2 × 10⁻¹ as a decimal. =
  33. 33.What is the value of (2/9)⁻¹? =
  34. 34.What is the value of 5³ × 5⁻⁶? =
  35. 35.Write 410 in standard form as 4.1 × 10ⁿ. What is n?
  36. 36.Write 5.8 × 10⁻¹ as a decimal. =
  37. 37.Write 7.5 × 10⁻¹ as a decimal. =
  38. 38.Write 6.9 × 10⁻³ as a decimal. =
  39. 39.Write (5⁸)⁹ as a single power 5ⁿ. What is n?
  40. 40.What is the value of 5⁻³ (as a fraction)? =

Answer key

  1. 30
  2. 0.055
  3. 125
  4. 81
  5. 35
  6. 5/3
  7. 8
  8. 2
  9. 12
  10. 6600000
  11. 0.0002
  12. 1
  13. 63000000
  14. 512
  15. 15
  16. 3400000
  17. 36/25
  18. 6
  19. 0.57
  20. 1/81
  21. 2
  22. 0.027
  23. 49
  24. 125
  25. 1/8
  26. 81
  27. 8192
  28. 0.0085
  29. 14
  30. 4200
  31. 1/343
  32. 0.92
  33. 9/2
  34. 1/125
  35. 2
  36. 0.58
  37. 0.75
  38. 0.0069
  39. 72
  40. 1/125

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