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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 836 · 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 3⁻⁶ (as a fraction)? =
  2. 2.Write 7.6 × 10⁻¹ as a decimal. =
  3. 3.What is the value of 7⁻³ (as a fraction)? =
  4. 4.What is the value of 3² × 3⁻¹? =
  5. 5.Write 7.5 × 10⁻³ as a decimal. =
  6. 6.Write 1,800 in standard form as 1.8 × 10ⁿ. What is n?
  7. 7.Write 2¹⁶ ÷ 2⁸ as a single power 2ⁿ. What is n?
  8. 8.What is the value of 2⁶? =
  9. 9.What is the value of 2⁵ × 2⁻²? =
  10. 10.What is the value of 9⁻² (as a fraction)? =
  11. 11.Write 2.1 × 10⁻² as a decimal. =
  12. 12.Write 4.3 × 10⁻⁴ as a decimal. =
  13. 13.What is the value of 5⁻⁴ (as a fraction)? =
  14. 14.Write 1.5 × 10⁻⁴ as a decimal. =
  15. 15.Write 2.3 × 10⁻¹ as a decimal. =
  16. 16.Write 7⁶ × 7² as a single power 7ⁿ. What is n?
  17. 17.What is the value of (4/7)⁻¹? =
  18. 18.What is the value of 5⁵ × 5⁻⁵? =
  19. 19.What is the value of 5⁶ × 5⁻²? =
  20. 20.Write 9.8 × 10⁻² as a decimal. =
  21. 21.What is the value of (2/5)⁻¹? =
  22. 22.What is the value of 3³ × 3⁻²? =
  23. 23.Write 1.5 × 10⁻¹ as a decimal. =
  24. 24.6.9 × 10⁷ =
  25. 25.What is the value of 10⁵ × 10⁻¹? =
  26. 26.What is the value of 3⁵ × 3⁻⁴? =
  27. 27.What is the value of 3⁶? =
  28. 28.What is the value of 5² × 5⁻²? =
  29. 29.Write 8.6 × 10⁻⁴ as a decimal. =
  30. 30.Write (2³)⁹ as a single power 2ⁿ. What is n?
  31. 31.8.5 × 10⁷ =
  32. 32.What is the value of 2⁷? =
  33. 33.9 × 10³ =
  34. 34.What is the value of 2⁻⁹ (as a fraction)? =
  35. 35.What is the value of 3⁻³ (as a fraction)? =
  36. 36.What is the value of 3³ × 3⁻⁴? =
  37. 37.Write 63,000 in standard form as 6.3 × 10ⁿ. What is n?
  38. 38.What is the value of 3⁻⁵ (as a fraction)? =
  39. 39.What is the value of 3⁶ × 3⁻¹? =
  40. 40.What is the value of 10² × 10⁻²? =

Answer key

  1. 1/729
  2. 0.76
  3. 1/343
  4. 3
  5. 0.0075
  6. 3
  7. 8
  8. 64
  9. 8
  10. 1/81
  11. 0.021
  12. 0.00043
  13. 1/625
  14. 0.00015
  15. 0.23
  16. 8
  17. 7/4
  18. 1
  19. 625
  20. 0.098
  21. 5/2
  22. 3
  23. 0.15
  24. 69000000
  25. 10000
  26. 3
  27. 729
  28. 1
  29. 0.00086
  30. 27
  31. 85000000
  32. 128
  33. 9000
  34. 1/512
  35. 1/27
  36. 1/3
  37. 4
  38. 1/243
  39. 243
  40. 1

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