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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 960 · 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 2¹² ÷ 2⁹ as a single power 2ⁿ. What is n?
  2. 2.What is the value of (1/4)⁻²? =
  3. 3.Write (4⁸)⁵ as a single power 4ⁿ. What is n?
  4. 4.What is the value of (5/9)⁻¹? =
  5. 5.What is the value of 3³ × 3⁻³? =
  6. 6.What is the value of 5⁴ × 5⁻¹? =
  7. 7.What is the value of (3/4)⁻²? =
  8. 8.Write (5⁹)⁵ as a single power 5ⁿ. What is n?
  9. 9.What is the value of 2⁻⁶ (as a fraction)? =
  10. 10.What is the value of 3⁻⁶ (as a fraction)? =
  11. 11.Write 9,90,00,000 in standard form as 9.9 × 10ⁿ. What is n?
  12. 12.What is the value of 3² × 3⁻²? =
  13. 13.Write 9⁹ ÷ 9⁴ as a single power 9ⁿ. What is n?
  14. 14.What is the value of 10⁴? =
  15. 15.What is the value of 6⁻¹ (as a fraction)? =
  16. 16.What is the value of 2² × 2⁻¹? =
  17. 17.What is the value of 5⁴ × 5⁻⁵? =
  18. 18.What is the value of (2/7)⁻¹? =
  19. 19.What is the value of (5/6)⁻²? =
  20. 20.What is the value of 5⁴ × 5⁻⁴? =
  21. 21.What is the value of 3² × 3⁻⁴? =
  22. 22.What is the value of 3⁻¹ (as a fraction)? =
  23. 23.Write 1.5 × 10⁻⁴ as a decimal. =
  24. 24.What is the value of (1/8)⁻¹? =
  25. 25.7.8 × 10⁷ =
  26. 26.What is the value of 8³? =
  27. 27.Write 2.9 × 10⁻³ as a decimal. =
  28. 28.What is the value of 9⁵? =
  29. 29.Write 3⁹ × 3⁵ as a single power 3ⁿ. What is n?
  30. 30.Write 4¹³ ÷ 4⁹ as a single power 4ⁿ. What is n?
  31. 31.What is the value of (2/5)⁻²? =
  32. 32.What is the value of 4⁴? =
  33. 33.What is the value of (3/5)⁻²? =
  34. 34.What is the value of (2/5)⁻¹? =
  35. 35.What is the value of 3⁸? =
  36. 36.What is the value of (7/8)⁻¹? =
  37. 37.Write (3⁶)⁹ as a single power 3ⁿ. What is n?
  38. 38.Write 7² × 7⁷ as a single power 7ⁿ. What is n?
  39. 39.What is the value of 10² × 10⁻⁴? =
  40. 40.Write 3.7 × 10⁻² as a decimal. =

Answer key

  1. 3
  2. 16
  3. 40
  4. 9/5
  5. 1
  6. 125
  7. 16/9
  8. 45
  9. 1/64
  10. 1/729
  11. 7
  12. 1
  13. 5
  14. 10000
  15. 1/6
  16. 2
  17. 1/5
  18. 7/2
  19. 36/25
  20. 1
  21. 1/9
  22. 1/3
  23. 0.00015
  24. 8
  25. 78000000
  26. 512
  27. 0.0029
  28. 59049
  29. 14
  30. 4
  31. 25/4
  32. 256
  33. 25/9
  34. 5/2
  35. 6561
  36. 8/7
  37. 54
  38. 9
  39. 1/100
  40. 0.037

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