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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 173 · 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 (9⁵)⁴ as a single power 9ⁿ. What is n?
  2. 2.What is the value of 2⁻⁵ (as a fraction)? =
  3. 3.Write 1.9 × 10⁻³ as a decimal. =
  4. 4.What is the value of 5⁴ × 5⁻⁶? =
  5. 5.What is the value of 5³ × 5⁻⁵? =
  6. 6.What is the value of 5¹ × 5⁻⁵? =
  7. 7.What is the value of 5² × 5⁻⁶? =
  8. 8.What is the value of 2³ × 2⁻¹? =
  9. 9.What is the value of (1/8)⁻²? =
  10. 10.Write 95,00,000 in standard form as 9.5 × 10ⁿ. What is n?
  11. 11.What is the value of 8³? =
  12. 12.Write 6¹⁰ ÷ 6⁷ as a single power 6ⁿ. What is n?
  13. 13.What is the value of (3/7)⁻²? =
  14. 14.Write 6.1 × 10⁻⁴ as a decimal. =
  15. 15.Write 9¹⁵ ÷ 9⁶ as a single power 9ⁿ. What is n?
  16. 16.What is the value of 2⁴ × 2⁻⁴? =
  17. 17.What is the value of (5/9)⁻²? =
  18. 18.Write 96,000 in standard form as 9.6 × 10ⁿ. What is n?
  19. 19.What is the value of 2³ × 2⁻⁶? =
  20. 20.What is the value of 6²? =
  21. 21.What is the value of 2³ × 2⁻³? =
  22. 22.What is the value of (3/5)⁻²? =
  23. 23.Write 7.2 × 10⁻³ as a decimal. =
  24. 24.Write 4¹¹ ÷ 4⁹ as a single power 4ⁿ. What is n?
  25. 25.What is the value of 9⁻² (as a fraction)? =
  26. 26.Write 6⁷ × 6⁸ as a single power 6ⁿ. What is n?
  27. 27.Write 8.9 × 10⁻⁴ as a decimal. =
  28. 28.3.4 × 10³ =
  29. 29.What is the value of (1/6)⁻²? =
  30. 30.What is the value of 2⁻⁹ (as a fraction)? =
  31. 31.What is the value of 3⁴ × 3⁻²? =
  32. 32.Write 2⁶ × 2⁶ as a single power 2ⁿ. What is n?
  33. 33.What is the value of 5¹ × 5⁻³? =
  34. 34.What is the value of 10⁵ × 10⁻⁵? =
  35. 35.Write 7⁸ ÷ 7⁴ as a single power 7ⁿ. What is n?
  36. 36.Write 2⁹ × 2⁵ as a single power 2ⁿ. What is n?
  37. 37.What is the value of 5² × 5⁻³? =
  38. 38.Write 9.7 × 10⁻¹ as a decimal. =
  39. 39.Write 1.5 × 10⁻¹ as a decimal. =
  40. 40.What is the value of 5¹ × 5⁻⁴? =

Answer key

  1. 20
  2. 1/32
  3. 0.0019
  4. 1/25
  5. 1/25
  6. 1/625
  7. 1/625
  8. 4
  9. 64
  10. 6
  11. 512
  12. 3
  13. 49/9
  14. 0.00061
  15. 9
  16. 1
  17. 81/25
  18. 4
  19. 1/8
  20. 36
  21. 1
  22. 25/9
  23. 0.0072
  24. 2
  25. 1/81
  26. 15
  27. 0.00089
  28. 3400
  29. 36
  30. 1/512
  31. 9
  32. 12
  33. 1/25
  34. 1
  35. 4
  36. 14
  37. 1/5
  38. 0.97
  39. 0.15
  40. 1/125

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