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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 651 · 40 sums
TalentJR

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 5⁵ × 5⁻⁶? =
  2. 2.Write 6⁶ ÷ 6³ as a single power 6ⁿ. What is n?
  3. 3.Write 2⁷ × 2⁷ as a single power 2ⁿ. What is n?
  4. 4.What is the value of 10⁴ × 10⁻³? =
  5. 5.What is the value of 5⁶ × 5⁻⁴? =
  6. 6.What is the value of 2³? =
  7. 7.What is the value of 3⁻⁵ (as a fraction)? =
  8. 8.Write 44,000 in standard form as 4.4 × 10ⁿ. What is n?
  9. 9.What is the value of 2¹⁶? =
  10. 10.What is the value of 2⁻⁸ (as a fraction)? =
  11. 11.What is the value of 2⁵ × 2⁻⁵? =
  12. 12.What is the value of 10⁶ × 10⁻²? =
  13. 13.8.8 × 10² =
  14. 14.Write (3⁴)⁷ as a single power 3ⁿ. What is n?
  15. 15.What is the value of 2⁶? =
  16. 16.Write 1,300 in standard form as 1.3 × 10ⁿ. What is n?
  17. 17.Write 9.2 × 10⁻² as a decimal. =
  18. 18.What is the value of 7⁵? =
  19. 19.What is the value of 9³? =
  20. 20.Write 7.2 × 10⁻⁴ as a decimal. =
  21. 21.What is the value of (2/9)⁻¹? =
  22. 22.Write 9⁷ × 9⁸ as a single power 9ⁿ. What is n?
  23. 23.What is the value of 7²? =
  24. 24.Write 4⁹ × 4⁸ as a single power 4ⁿ. What is n?
  25. 25.Write 8.3 × 10⁻⁴ as a decimal. =
  26. 26.Write (5⁹)⁶ as a single power 5ⁿ. What is n?
  27. 27.Write 6¹¹ ÷ 6⁸ as a single power 6ⁿ. What is n?
  28. 28.Write 4.2 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 3⁴ × 3⁻⁶? =
  30. 30.Write 4.1 × 10⁻³ as a decimal. =
  31. 31.What is the value of 3⁵? =
  32. 32.Write 3⁵ ÷ 3³ as a single power 3ⁿ. What is n?
  33. 33.What is the value of 5⁻⁴ (as a fraction)? =
  34. 34.What is the value of 2⁴ × 2⁻²? =
  35. 35.Write 4¹² ÷ 4⁹ as a single power 4ⁿ. What is n?
  36. 36.Write (6⁷)⁸ as a single power 6ⁿ. What is n?
  37. 37.What is the value of 10³ × 10⁻³? =
  38. 38.Write 6⁷ × 6² as a single power 6ⁿ. What is n?
  39. 39.What is the value of 5⁵? =
  40. 40.What is the value of 5³ × 5⁻⁵? =

Answer key

  1. 1/5
  2. 3
  3. 14
  4. 10
  5. 25
  6. 8
  7. 1/243
  8. 4
  9. 65536
  10. 1/256
  11. 1
  12. 10000
  13. 880
  14. 28
  15. 64
  16. 3
  17. 0.092
  18. 16807
  19. 729
  20. 0.00072
  21. 9/2
  22. 15
  23. 49
  24. 17
  25. 0.00083
  26. 54
  27. 3
  28. 0.42
  29. 1/9
  30. 0.0041
  31. 243
  32. 2
  33. 1/625
  34. 4
  35. 3
  36. 56
  37. 1
  38. 9
  39. 3125
  40. 1/25

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