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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 46 · 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 3² × 3⁶ as a single power 3ⁿ. What is n?
  2. 2.3.1 × 10² =
  3. 3.Write 53,000 in standard form as 5.3 × 10ⁿ. What is n?
  4. 4.Write 4⁵ × 4⁸ as a single power 4ⁿ. What is n?
  5. 5.What is the value of 10³ × 10⁻⁴? =
  6. 6.What is the value of (2/5)⁻²? =
  7. 7.What is the value of 3² × 3⁻⁴? =
  8. 8.What is the value of 5⁴? =
  9. 9.Write 3 × 10⁻¹ as a decimal. =
  10. 10.4.7 × 10³ =
  11. 11.Write 9.8 × 10⁻³ as a decimal. =
  12. 12.9.5 × 10⁶ =
  13. 13.What is the value of 10² × 10⁻¹? =
  14. 14.What is the value of 3³ × 3⁻⁶? =
  15. 15.Write 7² × 7⁵ as a single power 7ⁿ. What is n?
  16. 16.Write 7¹⁰ ÷ 7⁶ as a single power 7ⁿ. What is n?
  17. 17.Write 40,00,000 in standard form as 4 × 10ⁿ. What is n?
  18. 18.Write 5³ × 5⁴ as a single power 5ⁿ. What is n?
  19. 19.What is the value of 3¹ × 3⁻³? =
  20. 20.What is the value of 5² × 5⁻⁵? =
  21. 21.Write 9.3 × 10⁻¹ as a decimal. =
  22. 22.Write 1.3 × 10⁻⁴ as a decimal. =
  23. 23.What is the value of 2⁹? =
  24. 24.What is the value of (1/4)⁻²? =
  25. 25.What is the value of 5⁶ × 5⁻⁵? =
  26. 26.Write 63,000 in standard form as 6.3 × 10ⁿ. What is n?
  27. 27.Write 8.5 × 10⁻³ as a decimal. =
  28. 28.Write 2 × 10⁻¹ as a decimal. =
  29. 29.Write 3.8 × 10⁻³ as a decimal. =
  30. 30.What is the value of 6³? =
  31. 31.Write 2⁵ × 2³ as a single power 2ⁿ. What is n?
  32. 32.Write 3,30,000 in standard form as 3.3 × 10ⁿ. What is n?
  33. 33.What is the value of 10⁶ × 10⁻¹? =
  34. 34.Write 5.3 × 10⁻¹ as a decimal. =
  35. 35.Write 9.5 × 10⁻² as a decimal. =
  36. 36.What is the value of 2⁵ × 2⁻³? =
  37. 37.Write (2⁷)³ as a single power 2ⁿ. What is n?
  38. 38.Write 8.2 × 10⁻² as a decimal. =
  39. 39.Write 4.2 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of 10⁻¹ (as a fraction)? =

Answer key

  1. 8
  2. 310
  3. 4
  4. 13
  5. 1/10
  6. 25/4
  7. 1/9
  8. 625
  9. 0.3
  10. 4700
  11. 0.0098
  12. 9500000
  13. 10
  14. 1/27
  15. 7
  16. 4
  17. 6
  18. 7
  19. 1/9
  20. 1/125
  21. 0.93
  22. 0.00013
  23. 512
  24. 16
  25. 5
  26. 4
  27. 0.0085
  28. 0.2
  29. 0.0038
  30. 216
  31. 8
  32. 5
  33. 100000
  34. 0.53
  35. 0.095
  36. 4
  37. 21
  38. 0.082
  39. 0.00042
  40. 1/10

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