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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 103 · 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 6²? =
  2. 2.What is the value of 2³? =
  3. 3.What is the value of 3⁻⁵ (as a fraction)? =
  4. 4.What is the value of 6⁻¹ (as a fraction)? =
  5. 5.Write 6.2 × 10⁻¹ as a decimal. =
  6. 6.What is the value of 8³? =
  7. 7.Write 8.3 × 10⁻¹ as a decimal. =
  8. 8.What is the value of 2⁻¹ (as a fraction)? =
  9. 9.Write 9.2 × 10⁻⁴ as a decimal. =
  10. 10.Write 8¹⁷ ÷ 8⁸ as a single power 8ⁿ. What is n?
  11. 11.Write 3.7 × 10⁻³ as a decimal. =
  12. 12.Write 2.8 × 10⁻³ as a decimal. =
  13. 13.Write 4,200 in standard form as 4.2 × 10ⁿ. What is n?
  14. 14.What is the value of 6⁵? =
  15. 15.Write 3² × 3⁸ as a single power 3ⁿ. What is n?
  16. 16.What is the value of 2¹⁴? =
  17. 17.Write 9¹¹ ÷ 9⁸ as a single power 9ⁿ. What is n?
  18. 18.What is the value of 9⁻¹ (as a fraction)? =
  19. 19.What is the value of (1/8)⁻²? =
  20. 20.Write (6⁵)⁴ as a single power 6ⁿ. What is n?
  21. 21.What is the value of 5³ × 5⁻¹? =
  22. 22.What is the value of (1/5)⁻²? =
  23. 23.What is the value of 5⁴ × 5⁻¹? =
  24. 24.Write 2⁸ × 2⁹ as a single power 2ⁿ. What is n?
  25. 25.Write 4⁹ × 4⁷ as a single power 4ⁿ. What is n?
  26. 26.Write 9.4 × 10⁻¹ as a decimal. =
  27. 27.Write (7²)⁷ as a single power 7ⁿ. What is n?
  28. 28.Write 7¹⁴ ÷ 7⁵ as a single power 7ⁿ. What is n?
  29. 29.Write 6.5 × 10⁻² as a decimal. =
  30. 30.Write 8¹⁰ ÷ 8⁷ as a single power 8ⁿ. What is n?
  31. 31.What is the value of 5⁶ × 5⁻³? =
  32. 32.2.5 × 10⁴ =
  33. 33.Write (6⁶)⁵ as a single power 6ⁿ. What is n?
  34. 34.What is the value of (3/4)⁻¹? =
  35. 35.Write 9⁸ × 9⁴ as a single power 9ⁿ. What is n?
  36. 36.What is the value of 3⁻² (as a fraction)? =
  37. 37.What is the value of 2⁻² (as a fraction)? =
  38. 38.What is the value of (2/9)⁻²? =
  39. 39.What is the value of (1/3)⁻¹? =
  40. 40.What is the value of 2⁶ × 2⁻³? =

Answer key

  1. 36
  2. 8
  3. 1/243
  4. 1/6
  5. 0.62
  6. 512
  7. 0.83
  8. 1/2
  9. 0.00092
  10. 9
  11. 0.0037
  12. 0.0028
  13. 3
  14. 7776
  15. 10
  16. 16384
  17. 3
  18. 1/9
  19. 64
  20. 20
  21. 25
  22. 25
  23. 125
  24. 17
  25. 16
  26. 0.94
  27. 14
  28. 9
  29. 0.065
  30. 3
  31. 125
  32. 25000
  33. 30
  34. 4/3
  35. 12
  36. 1/9
  37. 1/4
  38. 81/4
  39. 3
  40. 8

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