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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 633 · 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.What is the value of 9⁻² (as a fraction)? =
  2. 2.Write 8.2 × 10⁻¹ as a decimal. =
  3. 3.Write 46,000 in standard form as 4.6 × 10ⁿ. What is n?
  4. 4.Write 2 × 10⁻¹ as a decimal. =
  5. 5.What is the value of 4⁻² (as a fraction)? =
  6. 6.Write 9¹¹ ÷ 9⁵ as a single power 9ⁿ. What is n?
  7. 7.Write 4³ × 4⁵ as a single power 4ⁿ. What is n?
  8. 8.What is the value of (1/9)⁻²? =
  9. 9.What is the value of 3² × 3⁻³? =
  10. 10.Write 5⁹ × 5² as a single power 5ⁿ. What is n?
  11. 11.Write 8.5 × 10⁻² as a decimal. =
  12. 12.What is the value of 2⁻¹ (as a fraction)? =
  13. 13.Write 7² × 7³ as a single power 7ⁿ. What is n?
  14. 14.What is the value of 5² × 5⁻³? =
  15. 15.Write 6¹⁵ ÷ 6⁹ as a single power 6ⁿ. What is n?
  16. 16.Write 7.6 × 10⁻² as a decimal. =
  17. 17.Write 3.6 × 10⁻³ as a decimal. =
  18. 18.Write 92,00,000 in standard form as 9.2 × 10ⁿ. What is n?
  19. 19.Write 20,000 in standard form as 2 × 10ⁿ. What is n?
  20. 20.Write (7³)⁸ as a single power 7ⁿ. What is n?
  21. 21.What is the value of 2⁵ × 2⁻⁶? =
  22. 22.Write 2.6 × 10⁻² as a decimal. =
  23. 23.What is the value of 2⁻³ (as a fraction)? =
  24. 24.What is the value of 4³? =
  25. 25.What is the value of 5⁵ × 5⁻⁵? =
  26. 26.What is the value of (3/7)⁻¹? =
  27. 27.3 × 10³ =
  28. 28.Write 6¹³ ÷ 6⁷ as a single power 6ⁿ. What is n?
  29. 29.Write 7.5 × 10⁻³ as a decimal. =
  30. 30.7.6 × 10² =
  31. 31.What is the value of 6⁻¹ (as a fraction)? =
  32. 32.Write 1.3 × 10⁻¹ as a decimal. =
  33. 33.Write 3.5 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 3⁵ × 3⁻⁶? =
  35. 35.2.6 × 10³ =
  36. 36.7.1 × 10⁷ =
  37. 37.What is the value of (3/5)⁻²? =
  38. 38.Write 3.8 × 10⁻⁴ as a decimal. =
  39. 39.What is the value of 2¹²? =
  40. 40.7 × 10⁵ =

Answer key

  1. 1/81
  2. 0.82
  3. 4
  4. 0.2
  5. 1/16
  6. 6
  7. 8
  8. 81
  9. 1/3
  10. 11
  11. 0.085
  12. 1/2
  13. 5
  14. 1/5
  15. 6
  16. 0.076
  17. 0.0036
  18. 6
  19. 4
  20. 24
  21. 1/2
  22. 0.026
  23. 1/8
  24. 64
  25. 1
  26. 7/3
  27. 3000
  28. 6
  29. 0.0075
  30. 760
  31. 1/6
  32. 0.13
  33. 0.35
  34. 1/3
  35. 2600
  36. 71000000
  37. 25/9
  38. 0.00038
  39. 4096
  40. 700000

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