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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 248 · 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 2 × 10⁻² as a decimal. =
  2. 2.Write 3 × 10⁻⁴ as a decimal. =
  3. 3.What is the value of 5³? =
  4. 4.What is the value of 2⁴ × 2⁻²? =
  5. 5.What is the value of 3³ × 3⁻³? =
  6. 6.What is the value of 3¹⁰? =
  7. 7.What is the value of 3⁻¹ (as a fraction)? =
  8. 8.Write 4⁶ × 4⁹ as a single power 4ⁿ. What is n?
  9. 9.What is the value of 5⁴ × 5⁻³? =
  10. 10.What is the value of 10⁵ × 10⁻¹? =
  11. 11.What is the value of 10⁴? =
  12. 12.Write 7.5 × 10⁻² as a decimal. =
  13. 13.Write 3 × 10⁻² as a decimal. =
  14. 14.Write 1.6 × 10⁻¹ as a decimal. =
  15. 15.Write 4.9 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 10⁶ × 10⁻⁴? =
  17. 17.Write 6.3 × 10⁻⁴ as a decimal. =
  18. 18.What is the value of 3⁸? =
  19. 19.Write 5.2 × 10⁻¹ as a decimal. =
  20. 20.9 × 10⁴ =
  21. 21.What is the value of 2⁻⁷ (as a fraction)? =
  22. 22.What is the value of 3² × 3⁻⁶? =
  23. 23.What is the value of (5/8)⁻¹? =
  24. 24.What is the value of (1/5)⁻¹? =
  25. 25.Write 44,000 in standard form as 4.4 × 10ⁿ. What is n?
  26. 26.Write 6.9 × 10⁻¹ as a decimal. =
  27. 27.What is the value of 10¹ × 10⁻²? =
  28. 28.Write 9.1 × 10⁻³ as a decimal. =
  29. 29.What is the value of 2²? =
  30. 30.What is the value of (1/2)⁻²? =
  31. 31.What is the value of (2/9)⁻²? =
  32. 32.What is the value of 2⁻³ (as a fraction)? =
  33. 33.Write (6²)⁹ as a single power 6ⁿ. What is n?
  34. 34.What is the value of 2³? =
  35. 35.Write (2⁴)⁸ as a single power 2ⁿ. What is n?
  36. 36.What is the value of 6⁵? =
  37. 37.What is the value of (3/4)⁻¹? =
  38. 38.What is the value of 3⁻⁶ (as a fraction)? =
  39. 39.What is the value of 3⁶ × 3⁻⁴? =
  40. 40.Write 6.8 × 10⁻² as a decimal. =

Answer key

  1. 0.02
  2. 0.0003
  3. 125
  4. 4
  5. 1
  6. 59049
  7. 1/3
  8. 15
  9. 5
  10. 10000
  11. 10000
  12. 0.075
  13. 0.03
  14. 0.16
  15. 0.00049
  16. 100
  17. 0.00063
  18. 6561
  19. 0.52
  20. 90000
  21. 1/128
  22. 1/81
  23. 8/5
  24. 5
  25. 4
  26. 0.69
  27. 1/10
  28. 0.0091
  29. 4
  30. 4
  31. 81/4
  32. 1/8
  33. 18
  34. 8
  35. 32
  36. 7776
  37. 4/3
  38. 1/729
  39. 9
  40. 0.068

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