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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 703 · 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 2⁶ ÷ 2³ as a single power 2ⁿ. What is n?
  2. 2.What is the value of 5²? =
  3. 3.What is the value of 3⁻⁶ (as a fraction)? =
  4. 4.What is the value of 3⁹? =
  5. 5.Write 7.1 × 10⁻¹ as a decimal. =
  6. 6.Write 2⁵ × 2⁴ as a single power 2ⁿ. What is n?
  7. 7.What is the value of 2³? =
  8. 8.What is the value of 3⁴ × 3⁻⁵? =
  9. 9.Write 4.2 × 10⁻¹ as a decimal. =
  10. 10.Write 2¹⁵ ÷ 2⁸ as a single power 2ⁿ. What is n?
  11. 11.Write (3⁴)⁶ as a single power 3ⁿ. What is n?
  12. 12.Write 3 × 10⁻² as a decimal. =
  13. 13.What is the value of (1/9)⁻¹? =
  14. 14.Write 9.4 × 10⁻⁴ as a decimal. =
  15. 15.9.7 × 10² =
  16. 16.7.7 × 10⁷ =
  17. 17.What is the value of 5³ × 5⁻²? =
  18. 18.What is the value of 2⁻¹ (as a fraction)? =
  19. 19.Write 3¹⁵ ÷ 3⁶ as a single power 3ⁿ. What is n?
  20. 20.What is the value of (5/9)⁻¹? =
  21. 21.Write 8.9 × 10⁻³ as a decimal. =
  22. 22.Write 2⁵ × 2⁶ as a single power 2ⁿ. What is n?
  23. 23.Write 6.5 × 10⁻² as a decimal. =
  24. 24.Write 9.7 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 6⁶? =
  26. 26.What is the value of 5² × 5⁻¹? =
  27. 27.What is the value of 5⁶ × 5⁻³? =
  28. 28.Write 9¹⁰ ÷ 9⁸ as a single power 9ⁿ. What is n?
  29. 29.What is the value of (3/5)⁻²? =
  30. 30.What is the value of 3⁻⁴ (as a fraction)? =
  31. 31.What is the value of (2/3)⁻¹? =
  32. 32.Write 9,100 in standard form as 9.1 × 10ⁿ. What is n?
  33. 33.What is the value of 2²? =
  34. 34.Write 510 in standard form as 5.1 × 10ⁿ. What is n?
  35. 35.What is the value of 6⁴? =
  36. 36.What is the value of 5³? =
  37. 37.What is the value of 3⁻² (as a fraction)? =
  38. 38.What is the value of 2¹⁰? =
  39. 39.Write 6⁴ × 6⁹ as a single power 6ⁿ. What is n?
  40. 40.Write (9⁴)⁷ as a single power 9ⁿ. What is n?

Answer key

  1. 3
  2. 25
  3. 1/729
  4. 19683
  5. 0.71
  6. 9
  7. 8
  8. 1/3
  9. 0.42
  10. 7
  11. 24
  12. 0.03
  13. 9
  14. 0.00094
  15. 970
  16. 77000000
  17. 5
  18. 1/2
  19. 9
  20. 9/5
  21. 0.0089
  22. 11
  23. 0.065
  24. 0.97
  25. 46656
  26. 5
  27. 125
  28. 2
  29. 25/9
  30. 1/81
  31. 3/2
  32. 3
  33. 4
  34. 2
  35. 1296
  36. 125
  37. 1/9
  38. 1024
  39. 13
  40. 28

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