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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 98 · 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.Write 3,800 in standard form as 3.8 × 10ⁿ. What is n?
  2. 2.Write 9 × 10⁻⁴ as a decimal. =
  3. 3.Write 5⁷ × 5⁸ as a single power 5ⁿ. What is n?
  4. 4.What is the value of 2⁻⁸ (as a fraction)? =
  5. 5.6.5 × 10⁴ =
  6. 6.What is the value of 10⁴ × 10⁻²? =
  7. 7.Write 7,000 in standard form as 7 × 10ⁿ. What is n?
  8. 8.Write 6.3 × 10⁻¹ as a decimal. =
  9. 9.What is the value of 2⁻³ (as a fraction)? =
  10. 10.What is the value of (1/6)⁻²? =
  11. 11.Write 1.5 × 10⁻³ as a decimal. =
  12. 12.Write 2,300 in standard form as 2.3 × 10ⁿ. What is n?
  13. 13.What is the value of 2⁻¹ (as a fraction)? =
  14. 14.Write 2.7 × 10⁻³ as a decimal. =
  15. 15.What is the value of 3⁷? =
  16. 16.Write 8¹² ÷ 8³ as a single power 8ⁿ. What is n?
  17. 17.Write 5.1 × 10⁻¹ as a decimal. =
  18. 18.Write 2⁵ × 2⁵ as a single power 2ⁿ. What is n?
  19. 19.Write 2.7 × 10⁻⁴ as a decimal. =
  20. 20.Write 3.3 × 10⁻² as a decimal. =
  21. 21.What is the value of 4²? =
  22. 22.Write (7³)⁴ as a single power 7ⁿ. What is n?
  23. 23.What is the value of (3/7)⁻²? =
  24. 24.What is the value of 2⁴ × 2⁻⁴? =
  25. 25.What is the value of 2⁷? =
  26. 26.Write 5,200 in standard form as 5.2 × 10ⁿ. What is n?
  27. 27.What is the value of 4⁸? =
  28. 28.What is the value of 5¹ × 5⁻¹? =
  29. 29.What is the value of 3¹⁰? =
  30. 30.Write (6⁸)⁵ as a single power 6ⁿ. What is n?
  31. 31.What is the value of 2²? =
  32. 32.Write 3.1 × 10⁻³ as a decimal. =
  33. 33.What is the value of 2² × 2⁻⁶? =
  34. 34.Write 22,000 in standard form as 2.2 × 10ⁿ. What is n?
  35. 35.Write 3⁷ ÷ 3³ as a single power 3ⁿ. What is n?
  36. 36.What is the value of 10⁴ × 10⁻³? =
  37. 37.Write 5 × 10⁻¹ as a decimal. =
  38. 38.Write 4⁹ × 4² as a single power 4ⁿ. What is n?
  39. 39.What is the value of 4⁵? =
  40. 40.4.8 × 10⁴ =

Answer key

  1. 3
  2. 0.0009
  3. 15
  4. 1/256
  5. 65000
  6. 100
  7. 3
  8. 0.63
  9. 1/8
  10. 36
  11. 0.0015
  12. 3
  13. 1/2
  14. 0.0027
  15. 2187
  16. 9
  17. 0.51
  18. 10
  19. 0.00027
  20. 0.033
  21. 16
  22. 12
  23. 49/9
  24. 1
  25. 128
  26. 3
  27. 65536
  28. 1
  29. 59049
  30. 40
  31. 4
  32. 0.0031
  33. 1/16
  34. 4
  35. 4
  36. 10
  37. 0.5
  38. 11
  39. 1024
  40. 48000

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