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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 801 · 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.What is the value of 2⁻¹ (as a fraction)? =
  2. 2.5.1 × 10⁵ =
  3. 3.Write 5¹⁷ ÷ 5⁸ as a single power 5ⁿ. What is n?
  4. 4.What is the value of 3²? =
  5. 5.Write 3⁸ × 3⁷ as a single power 3ⁿ. What is n?
  6. 6.What is the value of 9⁵? =
  7. 7.What is the value of (2/7)⁻²? =
  8. 8.Write 5.3 × 10⁻¹ as a decimal. =
  9. 9.Write 4² × 4⁶ as a single power 4ⁿ. What is n?
  10. 10.What is the value of 4⁵? =
  11. 11.What is the value of 2¹²? =
  12. 12.What is the value of 2¹⁶? =
  13. 13.Write (2⁷)² as a single power 2ⁿ. What is n?
  14. 14.What is the value of 2⁶ × 2⁻⁵? =
  15. 15.What is the value of 7⁻² (as a fraction)? =
  16. 16.Write 8.1 × 10⁻⁴ as a decimal. =
  17. 17.What is the value of 3¹⁰? =
  18. 18.Write 79,00,000 in standard form as 7.9 × 10ⁿ. What is n?
  19. 19.5.2 × 10² =
  20. 20.Write 7⁷ × 7⁸ as a single power 7ⁿ. What is n?
  21. 21.What is the value of 2⁻² (as a fraction)? =
  22. 22.What is the value of 2⁵? =
  23. 23.Write 59,00,000 in standard form as 5.9 × 10ⁿ. What is n?
  24. 24.6.9 × 10⁴ =
  25. 25.Write (4⁵)⁹ as a single power 4ⁿ. What is n?
  26. 26.What is the value of 2⁵ × 2⁻¹? =
  27. 27.What is the value of (4/9)⁻¹? =
  28. 28.Write 6.5 × 10⁻² as a decimal. =
  29. 29.What is the value of 10¹ × 10⁻⁵? =
  30. 30.What is the value of (1/2)⁻²? =
  31. 31.What is the value of (3/5)⁻¹? =
  32. 32.Write 2.2 × 10⁻¹ as a decimal. =
  33. 33.What is the value of (1/6)⁻²? =
  34. 34.Write 7.6 × 10⁻⁴ as a decimal. =
  35. 35.What is the value of 10⁵? =
  36. 36.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  37. 37.What is the value of (5/8)⁻¹? =
  38. 38.What is the value of 2¹ × 2⁻³? =
  39. 39.Write 8² × 8² as a single power 8ⁿ. What is n?
  40. 40.What is the value of 2⁻⁸ (as a fraction)? =

Answer key

  1. 1/2
  2. 510000
  3. 9
  4. 9
  5. 15
  6. 59049
  7. 49/4
  8. 0.53
  9. 8
  10. 1024
  11. 4096
  12. 65536
  13. 14
  14. 2
  15. 1/49
  16. 0.00081
  17. 59049
  18. 6
  19. 520
  20. 15
  21. 1/4
  22. 32
  23. 6
  24. 69000
  25. 45
  26. 16
  27. 9/4
  28. 0.065
  29. 1/10000
  30. 4
  31. 5/3
  32. 0.22
  33. 36
  34. 0.00076
  35. 100000
  36. 9
  37. 8/5
  38. 1/4
  39. 4
  40. 1/256

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