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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 321 · 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 2¹ × 2⁻¹? =
  2. 2.What is the value of 5⁻⁴ (as a fraction)? =
  3. 3.What is the value of (3/4)⁻¹? =
  4. 4.Write 2.3 × 10⁻³ as a decimal. =
  5. 5.What is the value of 10⁻³ (as a fraction)? =
  6. 6.Write 66,000 in standard form as 6.6 × 10ⁿ. What is n?
  7. 7.What is the value of 5⁵? =
  8. 8.What is the value of 5¹ × 5⁻¹? =
  9. 9.Write 3,300 in standard form as 3.3 × 10ⁿ. What is n?
  10. 10.What is the value of 6⁻¹ (as a fraction)? =
  11. 11.8.3 × 10³ =
  12. 12.Write 3 × 10⁻³ as a decimal. =
  13. 13.Write 1.3 × 10⁻⁴ as a decimal. =
  14. 14.6.2 × 10⁶ =
  15. 15.Write 9.4 × 10⁻² as a decimal. =
  16. 16.What is the value of 10² × 10⁻⁵? =
  17. 17.What is the value of 7⁴? =
  18. 18.What is the value of 3⁶ × 3⁻³? =
  19. 19.What is the value of 2⁻¹ (as a fraction)? =
  20. 20.Write 3.1 × 10⁻² as a decimal. =
  21. 21.What is the value of 6⁵? =
  22. 22.What is the value of (3/8)⁻¹? =
  23. 23.Write 5⁵ ÷ 5² as a single power 5ⁿ. What is n?
  24. 24.Write (6⁶)² as a single power 6ⁿ. What is n?
  25. 25.What is the value of 10⁴ × 10⁻²? =
  26. 26.What is the value of 2¹²? =
  27. 27.What is the value of 5³ × 5⁻²? =
  28. 28.Write 2⁵ × 2⁸ as a single power 2ⁿ. What is n?
  29. 29.What is the value of 2² × 2⁻⁵? =
  30. 30.What is the value of 2⁻³ (as a fraction)? =
  31. 31.1.3 × 10⁴ =
  32. 32.Write 4,60,000 in standard form as 4.6 × 10ⁿ. What is n?
  33. 33.4.5 × 10⁶ =
  34. 34.What is the value of 2⁹? =
  35. 35.What is the value of 3²? =
  36. 36.What is the value of 2⁻² (as a fraction)? =
  37. 37.Write 4⁴ × 4⁹ as a single power 4ⁿ. What is n?
  38. 38.What is the value of 3⁴ × 3⁻¹? =
  39. 39.What is the value of 8⁵? =
  40. 40.Write 6.5 × 10⁻¹ as a decimal. =

Answer key

  1. 1
  2. 1/625
  3. 4/3
  4. 0.0023
  5. 1/1000
  6. 4
  7. 3125
  8. 1
  9. 3
  10. 1/6
  11. 8300
  12. 0.003
  13. 0.00013
  14. 6200000
  15. 0.094
  16. 1/1000
  17. 2401
  18. 27
  19. 1/2
  20. 0.031
  21. 7776
  22. 8/3
  23. 3
  24. 12
  25. 100
  26. 4096
  27. 5
  28. 13
  29. 1/8
  30. 1/8
  31. 13000
  32. 5
  33. 4500000
  34. 512
  35. 9
  36. 1/4
  37. 13
  38. 27
  39. 32768
  40. 0.65

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