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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 554 · 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 1.9 × 10⁻⁴ as a decimal. =
  2. 2.4.7 × 10⁶ =
  3. 3.Write 3.6 × 10⁻¹ as a decimal. =
  4. 4.What is the value of 3¹ × 3⁻²? =
  5. 5.What is the value of 8⁵? =
  6. 6.Write 6.9 × 10⁻³ as a decimal. =
  7. 7.What is the value of 3⁻⁵ (as a fraction)? =
  8. 8.What is the value of 3⁵? =
  9. 9.What is the value of (7/9)⁻¹? =
  10. 10.What is the value of (5/6)⁻¹? =
  11. 11.Write 9.6 × 10⁻³ as a decimal. =
  12. 12.What is the value of 5⁶ × 5⁻⁴? =
  13. 13.What is the value of 10⁻² (as a fraction)? =
  14. 14.Write (5⁸)⁹ as a single power 5ⁿ. What is n?
  15. 15.What is the value of 5⁶ × 5⁻⁵? =
  16. 16.What is the value of (2/3)⁻²? =
  17. 17.What is the value of 5²? =
  18. 18.Write 9⁵ × 9³ as a single power 9ⁿ. What is n?
  19. 19.What is the value of (6/7)⁻²? =
  20. 20.Write 3² × 3⁵ as a single power 3ⁿ. What is n?
  21. 21.What is the value of 5¹ × 5⁻⁵? =
  22. 22.What is the value of 9⁵? =
  23. 23.Write 8.1 × 10⁻³ as a decimal. =
  24. 24.What is the value of 5³? =
  25. 25.Write 9⁸ × 9⁶ as a single power 9ⁿ. What is n?
  26. 26.Write 9¹³ ÷ 9⁴ as a single power 9ⁿ. What is n?
  27. 27.What is the value of 2⁴ × 2⁻⁵? =
  28. 28.Write 6,30,000 in standard form as 6.3 × 10ⁿ. What is n?
  29. 29.Write 4⁵ × 4³ as a single power 4ⁿ. What is n?
  30. 30.What is the value of 2³ × 2⁻⁶? =
  31. 31.What is the value of 9⁻³ (as a fraction)? =
  32. 32.Write 3¹⁴ ÷ 3⁵ as a single power 3ⁿ. What is n?
  33. 33.Write 4⁸ ÷ 4³ as a single power 4ⁿ. What is n?
  34. 34.8.7 × 10⁴ =
  35. 35.Write 2¹⁴ ÷ 2⁵ as a single power 2ⁿ. What is n?
  36. 36.What is the value of 10²? =
  37. 37.Write 72,00,000 in standard form as 7.2 × 10ⁿ. What is n?
  38. 38.Write 1.3 × 10⁻³ as a decimal. =
  39. 39.What is the value of 10⁵ × 10⁻²? =
  40. 40.Write 5.1 × 10⁻¹ as a decimal. =

Answer key

  1. 0.00019
  2. 4700000
  3. 0.36
  4. 1/3
  5. 32768
  6. 0.0069
  7. 1/243
  8. 243
  9. 9/7
  10. 6/5
  11. 0.0096
  12. 25
  13. 1/100
  14. 72
  15. 5
  16. 9/4
  17. 25
  18. 8
  19. 49/36
  20. 7
  21. 1/625
  22. 59049
  23. 0.0081
  24. 125
  25. 14
  26. 9
  27. 1/2
  28. 5
  29. 8
  30. 1/8
  31. 1/729
  32. 9
  33. 5
  34. 87000
  35. 9
  36. 100
  37. 6
  38. 0.0013
  39. 1000
  40. 0.51

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