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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 72 · 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 8.4 × 10⁻³ as a decimal. =
  2. 2.Write 30,000 in standard form as 3 × 10ⁿ. What is n?
  3. 3.Write 5⁶ ÷ 5² as a single power 5ⁿ. What is n?
  4. 4.Write 7⁴ × 7⁶ as a single power 7ⁿ. What is n?
  5. 5.Write 84,00,000 in standard form as 8.4 × 10ⁿ. What is n?
  6. 6.What is the value of 3⁴ × 3⁻⁵? =
  7. 7.What is the value of 3²? =
  8. 8.What is the value of 2⁻¹ (as a fraction)? =
  9. 9.What is the value of 2⁸? =
  10. 10.What is the value of 6⁴? =
  11. 11.Write 4.4 × 10⁻³ as a decimal. =
  12. 12.Write (9⁶)⁷ as a single power 9ⁿ. What is n?
  13. 13.What is the value of 2¹ × 2⁻⁵? =
  14. 14.What is the value of (1/3)⁻²? =
  15. 15.What is the value of 5⁶ × 5⁻¹? =
  16. 16.What is the value of 2⁻⁵ (as a fraction)? =
  17. 17.8.5 × 10² =
  18. 18.What is the value of 2¹ × 2⁻²? =
  19. 19.What is the value of 2⁵ × 2⁻³? =
  20. 20.Write 7.9 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 10³? =
  22. 22.What is the value of 9²? =
  23. 23.What is the value of 10⁴ × 10⁻⁶? =
  24. 24.Write 3.4 × 10⁻³ as a decimal. =
  25. 25.What is the value of 8⁻² (as a fraction)? =
  26. 26.What is the value of (3/7)⁻²? =
  27. 27.8.2 × 10⁵ =
  28. 28.What is the value of 2⁻² (as a fraction)? =
  29. 29.5.6 × 10⁶ =
  30. 30.Write 37,000 in standard form as 3.7 × 10ⁿ. What is n?
  31. 31.Write (8²)⁴ as a single power 8ⁿ. What is n?
  32. 32.Write (8⁹)⁸ as a single power 8ⁿ. What is n?
  33. 33.What is the value of 5⁷? =
  34. 34.Write (6⁵)³ as a single power 6ⁿ. What is n?
  35. 35.Write 9,90,00,000 in standard form as 9.9 × 10ⁿ. What is n?
  36. 36.What is the value of (5/8)⁻¹? =
  37. 37.What is the value of 2⁹? =
  38. 38.Write 25,000 in standard form as 2.5 × 10ⁿ. What is n?
  39. 39.What is the value of 2¹⁰? =
  40. 40.What is the value of 10⁴ × 10⁻³? =

Answer key

  1. 0.0084
  2. 4
  3. 4
  4. 10
  5. 6
  6. 1/3
  7. 9
  8. 1/2
  9. 256
  10. 1296
  11. 0.0044
  12. 42
  13. 1/16
  14. 9
  15. 3125
  16. 1/32
  17. 850
  18. 1/2
  19. 4
  20. 0.79
  21. 1000
  22. 81
  23. 1/100
  24. 0.0034
  25. 1/64
  26. 49/9
  27. 820000
  28. 1/4
  29. 5600000
  30. 4
  31. 8
  32. 72
  33. 78125
  34. 15
  35. 7
  36. 8/5
  37. 512
  38. 4
  39. 1024
  40. 10

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