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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 102 · 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.Write 8⁵ × 8⁹ as a single power 8ⁿ. What is n?
  2. 2.What is the value of 3⁴ × 3⁻³? =
  3. 3.Write (8³)⁹ as a single power 8ⁿ. What is n?
  4. 4.Write (8⁴)³ as a single power 8ⁿ. What is n?
  5. 5.Write (7⁹)⁹ as a single power 7ⁿ. What is n?
  6. 6.Write 3.6 × 10⁻³ as a decimal. =
  7. 7.3.2 × 10³ =
  8. 8.Write 910 in standard form as 9.1 × 10ⁿ. What is n?
  9. 9.What is the value of 4⁻³ (as a fraction)? =
  10. 10.What is the value of 10²? =
  11. 11.Write 8³ × 8² as a single power 8ⁿ. What is n?
  12. 12.What is the value of 2⁹? =
  13. 13.What is the value of 2⁵? =
  14. 14.What is the value of 8³? =
  15. 15.Write 3⁹ × 3⁶ as a single power 3ⁿ. What is n?
  16. 16.Write (6⁴)⁷ as a single power 6ⁿ. What is n?
  17. 17.What is the value of 7²? =
  18. 18.What is the value of 5¹ × 5⁻¹? =
  19. 19.Write 9.6 × 10⁻⁴ as a decimal. =
  20. 20.Write 8,000 in standard form as 8 × 10ⁿ. What is n?
  21. 21.Write 3.1 × 10⁻³ as a decimal. =
  22. 22.What is the value of (1/3)⁻¹? =
  23. 23.Write 1.1 × 10⁻¹ as a decimal. =
  24. 24.What is the value of 9⁴? =
  25. 25.What is the value of 2¹⁵? =
  26. 26.Write (2²)⁴ as a single power 2ⁿ. What is n?
  27. 27.Write 68,000 in standard form as 6.8 × 10ⁿ. What is n?
  28. 28.What is the value of 3⁴ × 3⁻⁴? =
  29. 29.7 × 10⁷ =
  30. 30.Write 2.8 × 10⁻¹ as a decimal. =
  31. 31.What is the value of 5⁴ × 5⁻⁴? =
  32. 32.Write 9.5 × 10⁻² as a decimal. =
  33. 33.Write 2.6 × 10⁻¹ as a decimal. =
  34. 34.Write 4¹¹ ÷ 4⁵ as a single power 4ⁿ. What is n?
  35. 35.What is the value of 2⁻⁶ (as a fraction)? =
  36. 36.What is the value of 6⁶? =
  37. 37.Write 9.4 × 10⁻¹ as a decimal. =
  38. 38.5.2 × 10⁶ =
  39. 39.What is the value of 3¹ × 3⁻⁴? =
  40. 40.What is the value of 2² × 2⁻³? =

Answer key

  1. 14
  2. 3
  3. 27
  4. 12
  5. 81
  6. 0.0036
  7. 3200
  8. 2
  9. 1/64
  10. 100
  11. 5
  12. 512
  13. 32
  14. 512
  15. 15
  16. 28
  17. 49
  18. 1
  19. 0.00096
  20. 3
  21. 0.0031
  22. 3
  23. 0.11
  24. 6561
  25. 32768
  26. 8
  27. 4
  28. 1
  29. 70000000
  30. 0.28
  31. 1
  32. 0.095
  33. 0.26
  34. 6
  35. 1/64
  36. 46656
  37. 0.94
  38. 5200000
  39. 1/27
  40. 1/2

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