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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 101 · 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 6.2 × 10⁻² as a decimal. =
  2. 2.What is the value of 2⁻⁹ (as a fraction)? =
  3. 3.What is the value of 8⁻³ (as a fraction)? =
  4. 4.What is the value of (1/2)⁻²? =
  5. 5.Write 8⁶ ÷ 8² as a single power 8ⁿ. What is n?
  6. 6.Write 7⁹ × 7⁸ as a single power 7ⁿ. What is n?
  7. 7.Write 9¹⁰ ÷ 9⁸ as a single power 9ⁿ. What is n?
  8. 8.Write 990 in standard form as 9.9 × 10ⁿ. What is n?
  9. 9.Write 1.7 × 10⁻³ as a decimal. =
  10. 10.Write 9.2 × 10⁻³ as a decimal. =
  11. 11.Write (7⁶)⁵ as a single power 7ⁿ. What is n?
  12. 12.Write 8⁴ × 8⁸ as a single power 8ⁿ. What is n?
  13. 13.7.7 × 10² =
  14. 14.1.9 × 10⁴ =
  15. 15.What is the value of 5⁴ × 5⁻⁵? =
  16. 16.What is the value of 3² × 3⁻¹? =
  17. 17.What is the value of 2¹³? =
  18. 18.What is the value of 9⁻¹ (as a fraction)? =
  19. 19.What is the value of 4⁷? =
  20. 20.What is the value of (2/9)⁻¹? =
  21. 21.Write 7 × 10⁻⁴ as a decimal. =
  22. 22.Write 1.8 × 10⁻³ as a decimal. =
  23. 23.What is the value of 5⁶ × 5⁻⁴? =
  24. 24.Write 8.8 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 3⁻⁵ (as a fraction)? =
  26. 26.What is the value of 2⁻⁵ (as a fraction)? =
  27. 27.2.9 × 10⁵ =
  28. 28.What is the value of 2⁵? =
  29. 29.What is the value of (1/6)⁻¹? =
  30. 30.5 × 10² =
  31. 31.Write 9¹² ÷ 9⁶ as a single power 9ⁿ. What is n?
  32. 32.What is the value of 3² × 3⁻²? =
  33. 33.Write 9.3 × 10⁻⁴ as a decimal. =
  34. 34.What is the value of 5⁶ × 5⁻⁵? =
  35. 35.Write 4 × 10⁻⁴ as a decimal. =
  36. 36.4.8 × 10⁷ =
  37. 37.Write 2.1 × 10⁻⁴ as a decimal. =
  38. 38.Write 4.1 × 10⁻³ as a decimal. =
  39. 39.Write 68,000 in standard form as 6.8 × 10ⁿ. What is n?
  40. 40.Write 3 × 10⁻⁴ as a decimal. =

Answer key

  1. 0.062
  2. 1/512
  3. 1/512
  4. 4
  5. 4
  6. 17
  7. 2
  8. 2
  9. 0.0017
  10. 0.0092
  11. 30
  12. 12
  13. 770
  14. 19000
  15. 1/5
  16. 3
  17. 8192
  18. 1/9
  19. 16384
  20. 9/2
  21. 0.0007
  22. 0.0018
  23. 25
  24. 0.88
  25. 1/243
  26. 1/32
  27. 290000
  28. 32
  29. 6
  30. 500
  31. 6
  32. 1
  33. 0.00093
  34. 5
  35. 0.0004
  36. 48000000
  37. 0.00021
  38. 0.0041
  39. 4
  40. 0.0003

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