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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 854 · 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 8.8 × 10⁻¹ as a decimal. =
  2. 2.7.7 × 10⁶ =
  3. 3.Write (3²)⁶ as a single power 3ⁿ. What is n?
  4. 4.What is the value of 8²? =
  5. 5.What is the value of 2⁴ × 2⁻¹? =
  6. 6.Write (4⁶)⁵ as a single power 4ⁿ. What is n?
  7. 7.6 × 10⁶ =
  8. 8.Write 7.7 × 10⁻¹ as a decimal. =
  9. 9.What is the value of 2⁹? =
  10. 10.What is the value of 5⁻⁴ (as a fraction)? =
  11. 11.What is the value of 2³ × 2⁻²? =
  12. 12.Write 4¹⁴ ÷ 4⁸ as a single power 4ⁿ. What is n?
  13. 13.Write 45,00,000 in standard form as 4.5 × 10ⁿ. What is n?
  14. 14.Write 31,000 in standard form as 3.1 × 10ⁿ. What is n?
  15. 15.Write 2,50,000 in standard form as 2.5 × 10ⁿ. What is n?
  16. 16.Write 4¹² ÷ 4³ as a single power 4ⁿ. What is n?
  17. 17.Write 4⁹ ÷ 4⁶ as a single power 4ⁿ. What is n?
  18. 18.What is the value of 4⁷? =
  19. 19.What is the value of (1/6)⁻¹? =
  20. 20.Write (7⁷)² as a single power 7ⁿ. What is n?
  21. 21.What is the value of 3² × 3⁻⁵? =
  22. 22.Write (3³)² as a single power 3ⁿ. What is n?
  23. 23.What is the value of 5⁵ × 5⁻⁶? =
  24. 24.Write 3¹⁰ ÷ 3⁵ as a single power 3ⁿ. What is n?
  25. 25.What is the value of 2⁻² (as a fraction)? =
  26. 26.What is the value of (5/8)⁻¹? =
  27. 27.What is the value of 2¹²? =
  28. 28.Write 7.3 × 10⁻³ as a decimal. =
  29. 29.Write 2,900 in standard form as 2.9 × 10ⁿ. What is n?
  30. 30.Write 7 × 10⁻³ as a decimal. =
  31. 31.7.1 × 10² =
  32. 32.What is the value of 5¹ × 5⁻²? =
  33. 33.Write 240 in standard form as 2.4 × 10ⁿ. What is n?
  34. 34.What is the value of 2⁸? =
  35. 35.What is the value of 3⁴? =
  36. 36.Write 8.7 × 10⁻² as a decimal. =
  37. 37.What is the value of 3⁻⁴ (as a fraction)? =
  38. 38.Write 6.7 × 10⁻⁴ as a decimal. =
  39. 39.What is the value of 2⁴ × 2⁻⁶? =
  40. 40.Write 7 × 10⁻² as a decimal. =

Answer key

  1. 0.88
  2. 7700000
  3. 12
  4. 64
  5. 8
  6. 30
  7. 6000000
  8. 0.77
  9. 512
  10. 1/625
  11. 2
  12. 6
  13. 6
  14. 4
  15. 5
  16. 9
  17. 3
  18. 16384
  19. 6
  20. 14
  21. 1/27
  22. 6
  23. 1/5
  24. 5
  25. 1/4
  26. 8/5
  27. 4096
  28. 0.0073
  29. 3
  30. 0.007
  31. 710
  32. 1/5
  33. 2
  34. 256
  35. 81
  36. 0.087
  37. 1/81
  38. 0.00067
  39. 1/4
  40. 0.07

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