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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 40 · 40 sums
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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 4⁹ × 4² as a single power 4ⁿ. What is n?
  2. 2.Write 3⁶ × 3⁸ as a single power 3ⁿ. What is n?
  3. 3.Write 2⁵ × 2⁵ as a single power 2ⁿ. What is n?
  4. 4.Write 4.2 × 10⁻¹ as a decimal. =
  5. 5.Write 5⁸ × 5³ as a single power 5ⁿ. What is n?
  6. 6.What is the value of 9⁻³ (as a fraction)? =
  7. 7.Write 1.2 × 10⁻⁴ as a decimal. =
  8. 8.Write 7 × 10⁻⁴ as a decimal. =
  9. 9.What is the value of 10⁵ × 10⁻⁴? =
  10. 10.7.1 × 10³ =
  11. 11.What is the value of 10⁻² (as a fraction)? =
  12. 12.Write 2.7 × 10⁻² as a decimal. =
  13. 13.What is the value of 6²? =
  14. 14.Write 3.2 × 10⁻³ as a decimal. =
  15. 15.Write 3⁷ × 3⁹ as a single power 3ⁿ. What is n?
  16. 16.3.5 × 10³ =
  17. 17.What is the value of 3⁷? =
  18. 18.Write 9.4 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 2¹⁰? =
  20. 20.Write 96,000 in standard form as 9.6 × 10ⁿ. What is n?
  21. 21.What is the value of 5³ × 5⁻⁴? =
  22. 22.What is the value of (2/3)⁻¹? =
  23. 23.Write 3.8 × 10⁻¹ as a decimal. =
  24. 24.Write 2,000 in standard form as 2 × 10ⁿ. What is n?
  25. 25.What is the value of 5¹ × 5⁻³? =
  26. 26.Write 1,60,00,000 in standard form as 1.6 × 10ⁿ. What is n?
  27. 27.What is the value of 3⁴? =
  28. 28.Write (6³)⁴ as a single power 6ⁿ. What is n?
  29. 29.What is the value of 5² × 5⁻³? =
  30. 30.Write 7⁵ × 7² as a single power 7ⁿ. What is n?
  31. 31.Write 5¹⁰ ÷ 5⁵ as a single power 5ⁿ. What is n?
  32. 32.What is the value of (5/6)⁻¹? =
  33. 33.What is the value of 3⁶? =
  34. 34.Write 1.9 × 10⁻³ as a decimal. =
  35. 35.Write 9,50,000 in standard form as 9.5 × 10ⁿ. What is n?
  36. 36.Write 2,700 in standard form as 2.7 × 10ⁿ. What is n?
  37. 37.Write 6.6 × 10⁻¹ as a decimal. =
  38. 38.What is the value of 2¹ × 2⁻⁶? =
  39. 39.Write 5⁶ ÷ 5⁴ as a single power 5ⁿ. What is n?
  40. 40.What is the value of (1/9)⁻¹? =

Answer key

  1. 11
  2. 14
  3. 10
  4. 0.42
  5. 11
  6. 1/729
  7. 0.00012
  8. 0.0007
  9. 10
  10. 7100
  11. 1/100
  12. 0.027
  13. 36
  14. 0.0032
  15. 16
  16. 3500
  17. 2187
  18. 0.00094
  19. 1024
  20. 4
  21. 1/5
  22. 3/2
  23. 0.38
  24. 3
  25. 1/25
  26. 7
  27. 81
  28. 12
  29. 1/5
  30. 7
  31. 5
  32. 6/5
  33. 729
  34. 0.0019
  35. 5
  36. 3
  37. 0.66
  38. 1/32
  39. 2
  40. 9

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