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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 118 · 40 sums
TalentJR

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.What is the value of (1/4)⁻¹? =
  2. 2.2.9 × 10⁷ =
  3. 3.What is the value of 2⁴ × 2⁻⁵? =
  4. 4.Write 2.5 × 10⁻² as a decimal. =
  5. 5.What is the value of 4⁻² (as a fraction)? =
  6. 6.2.8 × 10³ =
  7. 7.What is the value of 3³ × 3⁻¹? =
  8. 8.Write (5⁸)² as a single power 5ⁿ. What is n?
  9. 9.Write 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  10. 10.2.8 × 10² =
  11. 11.What is the value of 5⁴? =
  12. 12.What is the value of 6⁻³ (as a fraction)? =
  13. 13.What is the value of (3/5)⁻¹? =
  14. 14.What is the value of (1/3)⁻¹? =
  15. 15.What is the value of (4/9)⁻²? =
  16. 16.Write 8.3 × 10⁻² as a decimal. =
  17. 17.What is the value of 7²? =
  18. 18.What is the value of 2¹³? =
  19. 19.Write 6.4 × 10⁻² as a decimal. =
  20. 20.What is the value of 3²? =
  21. 21.What is the value of (1/4)⁻²? =
  22. 22.Write 4,700 in standard form as 4.7 × 10ⁿ. What is n?
  23. 23.What is the value of 2⁻⁷ (as a fraction)? =
  24. 24.Write (2⁶)⁷ as a single power 2ⁿ. What is n?
  25. 25.What is the value of 4⁵? =
  26. 26.Write 4⁵ × 4⁷ as a single power 4ⁿ. What is n?
  27. 27.What is the value of 10¹ × 10⁻¹? =
  28. 28.Write 4.9 × 10⁻² as a decimal. =
  29. 29.What is the value of 7⁻³ (as a fraction)? =
  30. 30.What is the value of 8⁴? =
  31. 31.What is the value of 2⁻² (as a fraction)? =
  32. 32.Write 8.8 × 10⁻² as a decimal. =
  33. 33.What is the value of 3⁻² (as a fraction)? =
  34. 34.What is the value of 3⁸? =
  35. 35.Write 4¹⁴ ÷ 4⁶ as a single power 4ⁿ. What is n?
  36. 36.6 × 10⁴ =
  37. 37.What is the value of 5⁶ × 5⁻¹? =
  38. 38.9.2 × 10³ =
  39. 39.Write 4⁸ ÷ 4⁶ as a single power 4ⁿ. What is n?
  40. 40.Write 240 in standard form as 2.4 × 10ⁿ. What is n?

Answer key

  1. 4
  2. 29000000
  3. 1/2
  4. 0.025
  5. 1/16
  6. 2800
  7. 9
  8. 16
  9. 3
  10. 280
  11. 625
  12. 1/216
  13. 5/3
  14. 3
  15. 81/16
  16. 0.083
  17. 49
  18. 8192
  19. 0.064
  20. 9
  21. 16
  22. 3
  23. 1/128
  24. 42
  25. 1024
  26. 12
  27. 1
  28. 0.049
  29. 1/343
  30. 4096
  31. 1/4
  32. 0.088
  33. 1/9
  34. 6561
  35. 8
  36. 60000
  37. 3125
  38. 9200
  39. 2
  40. 2

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