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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 474 · 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 2¹ × 2⁻³? =
  2. 2.What is the value of 9²? =
  3. 3.What is the value of 3⁻³ (as a fraction)? =
  4. 4.Write 8.3 × 10⁻⁴ as a decimal. =
  5. 5.Write (4⁶)³ as a single power 4ⁿ. What is n?
  6. 6.Write 5.1 × 10⁻¹ as a decimal. =
  7. 7.Write 7 × 10⁻² as a decimal. =
  8. 8.Write (4⁴)⁹ as a single power 4ⁿ. What is n?
  9. 9.What is the value of 6⁶? =
  10. 10.What is the value of 5³ × 5⁻⁴? =
  11. 11.Write 5⁴ × 5⁷ as a single power 5ⁿ. What is n?
  12. 12.Write 6.9 × 10⁻² as a decimal. =
  13. 13.What is the value of 10² × 10⁻⁴? =
  14. 14.Write 2.7 × 10⁻² as a decimal. =
  15. 15.Write 3¹⁰ ÷ 3² as a single power 3ⁿ. What is n?
  16. 16.What is the value of 10¹ × 10⁻²? =
  17. 17.Write (6²)⁶ as a single power 6ⁿ. What is n?
  18. 18.Write 6⁹ ÷ 6⁵ as a single power 6ⁿ. What is n?
  19. 19.What is the value of 2⁻⁵ (as a fraction)? =
  20. 20.Write 4.1 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 7⁻² (as a fraction)? =
  22. 22.What is the value of 8³? =
  23. 23.What is the value of 10⁻¹ (as a fraction)? =
  24. 24.What is the value of 3⁵ × 3⁻⁶? =
  25. 25.5.4 × 10⁶ =
  26. 26.Write 6¹⁴ ÷ 6⁶ as a single power 6ⁿ. What is n?
  27. 27.What is the value of 3² × 3⁻¹? =
  28. 28.What is the value of 7²? =
  29. 29.What is the value of 3²? =
  30. 30.What is the value of 10³ × 10⁻²? =
  31. 31.7.4 × 10⁷ =
  32. 32.Write 2 × 10⁻² as a decimal. =
  33. 33.Write 2,100 in standard form as 2.1 × 10ⁿ. What is n?
  34. 34.What is the value of 10⁻³ (as a fraction)? =
  35. 35.What is the value of 5⁷? =
  36. 36.What is the value of 3⁴ × 3⁻⁵? =
  37. 37.What is the value of 2⁵ × 2⁻²? =
  38. 38.What is the value of 5⁴ × 5⁻⁶? =
  39. 39.What is the value of 2⁷? =
  40. 40.Write 150 in standard form as 1.5 × 10ⁿ. What is n?

Answer key

  1. 1/4
  2. 81
  3. 1/27
  4. 0.00083
  5. 18
  6. 0.51
  7. 0.07
  8. 36
  9. 46656
  10. 1/5
  11. 11
  12. 0.069
  13. 1/100
  14. 0.027
  15. 8
  16. 1/10
  17. 12
  18. 4
  19. 1/32
  20. 0.41
  21. 1/49
  22. 512
  23. 1/10
  24. 1/3
  25. 5400000
  26. 8
  27. 3
  28. 49
  29. 9
  30. 10
  31. 74000000
  32. 0.02
  33. 3
  34. 1/1000
  35. 78125
  36. 1/3
  37. 8
  38. 1/25
  39. 128
  40. 2

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