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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 94 · 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 2⁵ × 2⁸ as a single power 2ⁿ. What is n?
  2. 2.What is the value of 10⁴? =
  3. 3.What is the value of 2¹ × 2⁻³? =
  4. 4.What is the value of 2⁻⁷ (as a fraction)? =
  5. 5.What is the value of 5²? =
  6. 6.What is the value of (2/3)⁻²? =
  7. 7.What is the value of 2⁵ × 2⁻³? =
  8. 8.8.7 × 10⁶ =
  9. 9.Write 3³ × 3⁸ as a single power 3ⁿ. What is n?
  10. 10.4.6 × 10⁴ =
  11. 11.What is the value of (6/7)⁻²? =
  12. 12.What is the value of 2³? =
  13. 13.What is the value of 4⁷? =
  14. 14.Write 8.4 × 10⁻⁴ as a decimal. =
  15. 15.What is the value of 5⁵ × 5⁻⁶? =
  16. 16.What is the value of (7/8)⁻²? =
  17. 17.Write 8.9 × 10⁻¹ as a decimal. =
  18. 18.Write 2.6 × 10⁻³ as a decimal. =
  19. 19.2.3 × 10² =
  20. 20.Write 7⁸ ÷ 7⁶ as a single power 7ⁿ. What is n?
  21. 21.What is the value of 2⁷? =
  22. 22.Write 4.6 × 10⁻¹ as a decimal. =
  23. 23.What is the value of 6⁶? =
  24. 24.6.5 × 10⁵ =
  25. 25.What is the value of 2⁻² (as a fraction)? =
  26. 26.Write 69,00,000 in standard form as 6.9 × 10ⁿ. What is n?
  27. 27.What is the value of 2⁻⁴ (as a fraction)? =
  28. 28.Write 2¹⁵ ÷ 2⁹ as a single power 2ⁿ. What is n?
  29. 29.Write 5,90,00,000 in standard form as 5.9 × 10ⁿ. What is n?
  30. 30.Write 5.2 × 10⁻¹ as a decimal. =
  31. 31.Write 2,00,00,000 in standard form as 2 × 10ⁿ. What is n?
  32. 32.Write 5.8 × 10⁻¹ as a decimal. =
  33. 33.What is the value of (2/5)⁻²? =
  34. 34.Write 380 in standard form as 3.8 × 10ⁿ. What is n?
  35. 35.What is the value of 2² × 2⁻³? =
  36. 36.What is the value of (2/9)⁻¹? =
  37. 37.What is the value of 4⁻³ (as a fraction)? =
  38. 38.Write 3.4 × 10⁻³ as a decimal. =
  39. 39.Write (7⁸)² as a single power 7ⁿ. What is n?
  40. 40.Write 3 × 10⁻⁴ as a decimal. =

Answer key

  1. 13
  2. 10000
  3. 1/4
  4. 1/128
  5. 25
  6. 9/4
  7. 4
  8. 8700000
  9. 11
  10. 46000
  11. 49/36
  12. 8
  13. 16384
  14. 0.00084
  15. 1/5
  16. 64/49
  17. 0.89
  18. 0.0026
  19. 230
  20. 2
  21. 128
  22. 0.46
  23. 46656
  24. 650000
  25. 1/4
  26. 6
  27. 1/16
  28. 6
  29. 7
  30. 0.52
  31. 7
  32. 0.58
  33. 25/4
  34. 2
  35. 1/2
  36. 9/2
  37. 1/64
  38. 0.0034
  39. 16
  40. 0.0003

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