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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 754 · 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 8⁷ × 8⁷ as a single power 8ⁿ. What is n?
  2. 2.Write 78,000 in standard form as 7.8 × 10ⁿ. What is n?
  3. 3.What is the value of 3² × 3⁻¹? =
  4. 4.What is the value of 2⁵ × 2⁻⁶? =
  5. 5.What is the value of 10³ × 10⁻²? =
  6. 6.Write 7,70,00,000 in standard form as 7.7 × 10ⁿ. What is n?
  7. 7.What is the value of (1/7)⁻²? =
  8. 8.What is the value of 3² × 3⁻⁵? =
  9. 9.What is the value of 6²? =
  10. 10.Write 4.4 × 10⁻² as a decimal. =
  11. 11.What is the value of 2³ × 2⁻³? =
  12. 12.What is the value of 5⁶ × 5⁻³? =
  13. 13.9.8 × 10⁷ =
  14. 14.What is the value of 5² × 5⁻¹? =
  15. 15.Write 5.1 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 3⁻² (as a fraction)? =
  17. 17.What is the value of (1/4)⁻²? =
  18. 18.What is the value of 10⁵ × 10⁻¹? =
  19. 19.Write 6⁷ ÷ 6³ as a single power 6ⁿ. What is n?
  20. 20.What is the value of 3³? =
  21. 21.What is the value of 5⁵ × 5⁻¹? =
  22. 22.What is the value of 2¹⁰? =
  23. 23.What is the value of (2/3)⁻¹? =
  24. 24.What is the value of 2¹ × 2⁻²? =
  25. 25.What is the value of 2⁶? =
  26. 26.What is the value of 3⁵ × 3⁻⁵? =
  27. 27.What is the value of 3⁻¹ (as a fraction)? =
  28. 28.What is the value of 4⁷? =
  29. 29.Write 8⁶ × 8⁷ as a single power 8ⁿ. What is n?
  30. 30.What is the value of 5⁵ × 5⁻³? =
  31. 31.Write 4.2 × 10⁻³ as a decimal. =
  32. 32.Write 2.5 × 10⁻⁴ as a decimal. =
  33. 33.Write 380 in standard form as 3.8 × 10ⁿ. What is n?
  34. 34.9.5 × 10⁶ =
  35. 35.Write 8⁹ × 8⁷ as a single power 8ⁿ. What is n?
  36. 36.Write (5⁴)² as a single power 5ⁿ. What is n?
  37. 37.What is the value of 2¹ × 2⁻⁵? =
  38. 38.What is the value of 10³ × 10⁻³? =
  39. 39.What is the value of 6⁻¹ (as a fraction)? =
  40. 40.What is the value of (5/8)⁻²? =

Answer key

  1. 14
  2. 4
  3. 3
  4. 1/2
  5. 10
  6. 7
  7. 49
  8. 1/27
  9. 36
  10. 0.044
  11. 1
  12. 125
  13. 98000000
  14. 5
  15. 0.00051
  16. 1/9
  17. 16
  18. 10000
  19. 4
  20. 27
  21. 625
  22. 1024
  23. 3/2
  24. 1/2
  25. 64
  26. 1
  27. 1/3
  28. 16384
  29. 13
  30. 25
  31. 0.0042
  32. 0.00025
  33. 2
  34. 9500000
  35. 16
  36. 8
  37. 1/16
  38. 1
  39. 1/6
  40. 64/25

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