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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 329 · 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 3² × 3⁻⁵? =
  2. 2.Write 250 in standard form as 2.5 × 10ⁿ. What is n?
  3. 3.What is the value of 2⁵ × 2⁻⁶? =
  4. 4.Write 3.6 × 10⁻¹ as a decimal. =
  5. 5.What is the value of 7⁻³ (as a fraction)? =
  6. 6.Write 5.5 × 10⁻⁴ as a decimal. =
  7. 7.Write 420 in standard form as 4.2 × 10ⁿ. What is n?
  8. 8.Write 7.3 × 10⁻³ as a decimal. =
  9. 9.Write 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  10. 10.Write 5.6 × 10⁻² as a decimal. =
  11. 11.Write 27,000 in standard form as 2.7 × 10ⁿ. What is n?
  12. 12.Write 8.9 × 10⁻³ as a decimal. =
  13. 13.Write 2.6 × 10⁻⁴ as a decimal. =
  14. 14.Write 1.2 × 10⁻³ as a decimal. =
  15. 15.Write 2⁸ × 2⁷ as a single power 2ⁿ. What is n?
  16. 16.What is the value of (5/7)⁻¹? =
  17. 17.What is the value of 6⁻² (as a fraction)? =
  18. 18.Write 4² × 4⁴ as a single power 4ⁿ. What is n?
  19. 19.What is the value of 3⁵? =
  20. 20.What is the value of 2¹³? =
  21. 21.What is the value of 10⁴ × 10⁻⁶? =
  22. 22.What is the value of 3¹ × 3⁻²? =
  23. 23.What is the value of 6⁵? =
  24. 24.What is the value of 3²? =
  25. 25.Write 3.5 × 10⁻⁴ as a decimal. =
  26. 26.What is the value of (1/6)⁻²? =
  27. 27.Write 2.1 × 10⁻¹ as a decimal. =
  28. 28.What is the value of 4⁴? =
  29. 29.What is the value of (2/7)⁻¹? =
  30. 30.What is the value of 2⁶? =
  31. 31.Write 2⁹ × 2⁸ as a single power 2ⁿ. What is n?
  32. 32.What is the value of 10² × 10⁻⁴? =
  33. 33.What is the value of 5⁻² (as a fraction)? =
  34. 34.Write 6⁸ ÷ 6⁵ as a single power 6ⁿ. What is n?
  35. 35.What is the value of 6⁶? =
  36. 36.What is the value of 3² × 3⁻¹? =
  37. 37.Write 2.9 × 10⁻³ as a decimal. =
  38. 38.Write 6⁹ ÷ 6⁶ as a single power 6ⁿ. What is n?
  39. 39.What is the value of 10⁴? =
  40. 40.What is the value of (6/7)⁻²? =

Answer key

  1. 1/27
  2. 2
  3. 1/2
  4. 0.36
  5. 1/343
  6. 0.00055
  7. 2
  8. 0.0073
  9. 3
  10. 0.056
  11. 4
  12. 0.0089
  13. 0.00026
  14. 0.0012
  15. 15
  16. 7/5
  17. 1/36
  18. 6
  19. 243
  20. 8192
  21. 1/100
  22. 1/3
  23. 7776
  24. 9
  25. 0.00035
  26. 36
  27. 0.21
  28. 256
  29. 7/2
  30. 64
  31. 17
  32. 1/100
  33. 1/25
  34. 3
  35. 46656
  36. 3
  37. 0.0029
  38. 3
  39. 10000
  40. 49/36

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