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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 48 · 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.Write (7⁵)⁸ as a single power 7ⁿ. What is n?
  2. 2.8 × 10² =
  3. 3.Write 6.1 × 10⁻¹ as a decimal. =
  4. 4.Write 2.1 × 10⁻² as a decimal. =
  5. 5.What is the value of (1/5)⁻²? =
  6. 6.What is the value of 6⁴? =
  7. 7.What is the value of 2⁵ × 2⁻¹? =
  8. 8.What is the value of 3² × 3⁻¹? =
  9. 9.What is the value of 5⁴ × 5⁻²? =
  10. 10.What is the value of 2³? =
  11. 11.Write 1.5 × 10⁻¹ as a decimal. =
  12. 12.What is the value of 5⁵? =
  13. 13.Write 3⁹ ÷ 3³ as a single power 3ⁿ. What is n?
  14. 14.What is the value of 3⁹? =
  15. 15.Write 6.3 × 10⁻² as a decimal. =
  16. 16.4.1 × 10⁴ =
  17. 17.What is the value of 10⁶ × 10⁻²? =
  18. 18.What is the value of 3⁻⁴ (as a fraction)? =
  19. 19.Write 97,000 in standard form as 9.7 × 10ⁿ. What is n?
  20. 20.What is the value of (2/5)⁻¹? =
  21. 21.What is the value of 2⁶ × 2⁻⁴? =
  22. 22.What is the value of (2/3)⁻¹? =
  23. 23.What is the value of 2¹ × 2⁻¹? =
  24. 24.What is the value of 10⁴? =
  25. 25.What is the value of 3⁵ × 3⁻⁵? =
  26. 26.What is the value of 5⁵ × 5⁻²? =
  27. 27.What is the value of 6³? =
  28. 28.What is the value of 2²? =
  29. 29.What is the value of 5⁶ × 5⁻⁵? =
  30. 30.What is the value of 6⁵? =
  31. 31.What is the value of 2⁻⁸ (as a fraction)? =
  32. 32.8.4 × 10² =
  33. 33.Write 7¹⁰ ÷ 7⁴ as a single power 7ⁿ. What is n?
  34. 34.What is the value of 8⁻¹ (as a fraction)? =
  35. 35.Write 4¹⁴ ÷ 4⁵ as a single power 4ⁿ. What is n?
  36. 36.Write 2.9 × 10⁻¹ as a decimal. =
  37. 37.What is the value of 6⁻¹ (as a fraction)? =
  38. 38.What is the value of 2¹⁰? =
  39. 39.What is the value of 5² × 5⁻⁵? =
  40. 40.What is the value of 2⁶? =

Answer key

  1. 40
  2. 800
  3. 0.61
  4. 0.021
  5. 25
  6. 1296
  7. 16
  8. 3
  9. 25
  10. 8
  11. 0.15
  12. 3125
  13. 6
  14. 19683
  15. 0.063
  16. 41000
  17. 10000
  18. 1/81
  19. 4
  20. 5/2
  21. 4
  22. 3/2
  23. 1
  24. 10000
  25. 1
  26. 125
  27. 216
  28. 4
  29. 5
  30. 7776
  31. 1/256
  32. 840
  33. 6
  34. 1/8
  35. 9
  36. 0.29
  37. 1/6
  38. 1024
  39. 1/125
  40. 64

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