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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 975 · 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 (1/9)⁻²? =
  2. 2.What is the value of (1/4)⁻²? =
  3. 3.Write 1.5 × 10⁻¹ as a decimal. =
  4. 4.What is the value of (4/5)⁻²? =
  5. 5.What is the value of 2¹⁰? =
  6. 6.What is the value of 2⁹? =
  7. 7.What is the value of 2³ × 2⁻²? =
  8. 8.Write 5,000 in standard form as 5 × 10ⁿ. What is n?
  9. 9.What is the value of 5⁷? =
  10. 10.Write 4⁴ × 4² as a single power 4ⁿ. What is n?
  11. 11.Write (9⁸)⁹ as a single power 9ⁿ. What is n?
  12. 12.Write 1.2 × 10⁻³ as a decimal. =
  13. 13.Write 3.5 × 10⁻² as a decimal. =
  14. 14.Write 2⁸ × 2³ as a single power 2ⁿ. What is n?
  15. 15.What is the value of 5⁻³ (as a fraction)? =
  16. 16.What is the value of 6⁴? =
  17. 17.2.5 × 10³ =
  18. 18.What is the value of 2¹ × 2⁻¹? =
  19. 19.7.2 × 10⁷ =
  20. 20.What is the value of (2/5)⁻²? =
  21. 21.Write 2⁸ × 2⁵ as a single power 2ⁿ. What is n?
  22. 22.What is the value of (1/8)⁻¹? =
  23. 23.4.6 × 10² =
  24. 24.What is the value of 2⁷? =
  25. 25.What is the value of 5¹ × 5⁻⁵? =
  26. 26.What is the value of 8⁴? =
  27. 27.Write 38,000 in standard form as 3.8 × 10ⁿ. What is n?
  28. 28.What is the value of 3⁵ × 3⁻⁶? =
  29. 29.Write 2¹⁴ ÷ 2⁶ as a single power 2ⁿ. What is n?
  30. 30.What is the value of 4⁸? =
  31. 31.What is the value of 9³? =
  32. 32.What is the value of 5²? =
  33. 33.What is the value of 2⁴ × 2⁻³? =
  34. 34.Write 7¹² ÷ 7⁹ as a single power 7ⁿ. What is n?
  35. 35.Write 2.8 × 10⁻⁴ as a decimal. =
  36. 36.What is the value of 4⁵? =
  37. 37.Write 60,000 in standard form as 6 × 10ⁿ. What is n?
  38. 38.Write 7.3 × 10⁻² as a decimal. =
  39. 39.What is the value of 3⁻¹ (as a fraction)? =
  40. 40.What is the value of 5⁶ × 5⁻²? =

Answer key

  1. 81
  2. 16
  3. 0.15
  4. 25/16
  5. 1024
  6. 512
  7. 2
  8. 3
  9. 78125
  10. 6
  11. 72
  12. 0.0012
  13. 0.035
  14. 11
  15. 1/125
  16. 1296
  17. 2500
  18. 1
  19. 72000000
  20. 25/4
  21. 13
  22. 8
  23. 460
  24. 128
  25. 1/625
  26. 4096
  27. 4
  28. 1/3
  29. 8
  30. 65536
  31. 729
  32. 25
  33. 2
  34. 3
  35. 0.00028
  36. 1024
  37. 4
  38. 0.073
  39. 1/3
  40. 625

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