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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 944 · 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 (8⁷)⁹ as a single power 8ⁿ. What is n?
  2. 2.What is the value of 5⁵ × 5⁻²? =
  3. 3.5.1 × 10⁵ =
  4. 4.Write (9⁶)⁴ as a single power 9ⁿ. What is n?
  5. 5.What is the value of (1/3)⁻²? =
  6. 6.What is the value of 3⁻⁴ (as a fraction)? =
  7. 7.What is the value of 10⁶ × 10⁻²? =
  8. 8.What is the value of 10³ × 10⁻⁵? =
  9. 9.Write 9.9 × 10⁻² as a decimal. =
  10. 10.Write (6⁷)⁵ as a single power 6ⁿ. What is n?
  11. 11.Write 42,00,000 in standard form as 4.2 × 10ⁿ. What is n?
  12. 12.What is the value of 2² × 2⁻²? =
  13. 13.Write 4.7 × 10⁻¹ as a decimal. =
  14. 14.Write 4.7 × 10⁻³ as a decimal. =
  15. 15.What is the value of (2/5)⁻²? =
  16. 16.What is the value of (2/5)⁻¹? =
  17. 17.4.3 × 10⁷ =
  18. 18.Write 6⁶ × 6³ as a single power 6ⁿ. What is n?
  19. 19.3.3 × 10⁴ =
  20. 20.Write 4,800 in standard form as 4.8 × 10ⁿ. What is n?
  21. 21.What is the value of 3² × 3⁻²? =
  22. 22.1.1 × 10⁷ =
  23. 23.What is the value of 4⁻² (as a fraction)? =
  24. 24.What is the value of 10²? =
  25. 25.Write 9.8 × 10⁻² as a decimal. =
  26. 26.What is the value of 5² × 5⁻⁴? =
  27. 27.Write 3.5 × 10⁻¹ as a decimal. =
  28. 28.What is the value of (4/9)⁻²? =
  29. 29.8.7 × 10⁷ =
  30. 30.What is the value of 2⁷? =
  31. 31.What is the value of 7⁻³ (as a fraction)? =
  32. 32.What is the value of (1/3)⁻¹? =
  33. 33.What is the value of (4/5)⁻²? =
  34. 34.Write 1.2 × 10⁻³ as a decimal. =
  35. 35.Write 2.7 × 10⁻² as a decimal. =
  36. 36.Write (3⁴)⁸ as a single power 3ⁿ. What is n?
  37. 37.What is the value of (1/7)⁻¹? =
  38. 38.Write 6 × 10⁻² as a decimal. =
  39. 39.Write 74,000 in standard form as 7.4 × 10ⁿ. What is n?
  40. 40.What is the value of 3⁶ × 3⁻⁵? =

Answer key

  1. 63
  2. 125
  3. 510000
  4. 24
  5. 9
  6. 1/81
  7. 10000
  8. 1/100
  9. 0.099
  10. 35
  11. 6
  12. 1
  13. 0.47
  14. 0.0047
  15. 25/4
  16. 5/2
  17. 43000000
  18. 9
  19. 33000
  20. 3
  21. 1
  22. 11000000
  23. 1/16
  24. 100
  25. 0.098
  26. 1/25
  27. 0.35
  28. 81/16
  29. 87000000
  30. 128
  31. 1/343
  32. 3
  33. 25/16
  34. 0.0012
  35. 0.027
  36. 32
  37. 7
  38. 0.06
  39. 4
  40. 3

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