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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 945 · 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 5⁸ × 5⁶ as a single power 5ⁿ. What is n?
  2. 2.3.5 × 10² =
  3. 3.Write 5.4 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of 5⁻⁴ (as a fraction)? =
  5. 5.What is the value of 2¹⁰? =
  6. 6.6.7 × 10² =
  7. 7.Write 3² × 3³ as a single power 3ⁿ. What is n?
  8. 8.Write (2⁶)⁸ as a single power 2ⁿ. What is n?
  9. 9.Write 5.9 × 10⁻¹ as a decimal. =
  10. 10.What is the value of (4/5)⁻²? =
  11. 11.Write 360 in standard form as 3.6 × 10ⁿ. What is n?
  12. 12.Write 9 × 10⁻¹ as a decimal. =
  13. 13.What is the value of 4³? =
  14. 14.Write (9⁶)⁵ as a single power 9ⁿ. What is n?
  15. 15.Write 1.3 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 5² × 5⁻⁵? =
  17. 17.Write 4.5 × 10⁻² as a decimal. =
  18. 18.What is the value of 5³ × 5⁻³? =
  19. 19.Write 8.5 × 10⁻⁴ as a decimal. =
  20. 20.What is the value of 2⁹? =
  21. 21.Write 4¹⁵ ÷ 4⁹ as a single power 4ⁿ. What is n?
  22. 22.Write 8¹⁰ ÷ 8⁵ as a single power 8ⁿ. What is n?
  23. 23.What is the value of 8⁻¹ (as a fraction)? =
  24. 24.What is the value of 2⁶ × 2⁻²? =
  25. 25.Write 9⁸ × 9² as a single power 9ⁿ. What is n?
  26. 26.Write 6⁹ × 6⁶ as a single power 6ⁿ. What is n?
  27. 27.4.9 × 10³ =
  28. 28.Write 6 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 3⁴ × 3⁻³? =
  30. 30.What is the value of 2⁶? =
  31. 31.What is the value of (1/4)⁻¹? =
  32. 32.What is the value of (5/8)⁻¹? =
  33. 33.What is the value of 4⁻³ (as a fraction)? =
  34. 34.What is the value of (3/8)⁻²? =
  35. 35.Write 4.8 × 10⁻¹ as a decimal. =
  36. 36.Write (3⁴)⁵ as a single power 3ⁿ. What is n?
  37. 37.6 × 10⁶ =
  38. 38.What is the value of 3¹ × 3⁻³? =
  39. 39.Write 3¹³ ÷ 3⁴ as a single power 3ⁿ. What is n?
  40. 40.Write 2³ × 2⁵ as a single power 2ⁿ. What is n?

Answer key

  1. 14
  2. 350
  3. 0.00054
  4. 1/625
  5. 1024
  6. 670
  7. 5
  8. 48
  9. 0.59
  10. 25/16
  11. 2
  12. 0.9
  13. 64
  14. 30
  15. 0.00013
  16. 1/125
  17. 0.045
  18. 1
  19. 0.00085
  20. 512
  21. 6
  22. 5
  23. 1/8
  24. 16
  25. 10
  26. 15
  27. 4900
  28. 0.6
  29. 3
  30. 64
  31. 4
  32. 8/5
  33. 1/64
  34. 64/9
  35. 0.48
  36. 20
  37. 6000000
  38. 1/9
  39. 9
  40. 8

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