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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 831 · 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 7,500 in standard form as 7.5 × 10ⁿ. What is n?
  2. 2.Write 5,30,000 in standard form as 5.3 × 10ⁿ. What is n?
  3. 3.3.4 × 10³ =
  4. 4.What is the value of 10² × 10⁻¹? =
  5. 5.What is the value of 4⁴? =
  6. 6.What is the value of 2¹ × 2⁻²? =
  7. 7.What is the value of 7⁻¹ (as a fraction)? =
  8. 8.What is the value of 10³ × 10⁻²? =
  9. 9.Write 6⁹ × 6⁵ as a single power 6ⁿ. What is n?
  10. 10.What is the value of 9⁴? =
  11. 11.What is the value of 2⁻⁸ (as a fraction)? =
  12. 12.What is the value of 5⁴? =
  13. 13.What is the value of 2² × 2⁻⁴? =
  14. 14.What is the value of 5⁶? =
  15. 15.Write (6³)⁴ as a single power 6ⁿ. What is n?
  16. 16.Write 8⁶ × 8⁹ as a single power 8ⁿ. What is n?
  17. 17.Write 6⁴ × 6⁹ as a single power 6ⁿ. What is n?
  18. 18.What is the value of 5⁻¹ (as a fraction)? =
  19. 19.What is the value of (3/4)⁻¹? =
  20. 20.What is the value of 3⁶ × 3⁻⁴? =
  21. 21.What is the value of 2⁶ × 2⁻²? =
  22. 22.What is the value of 6⁶? =
  23. 23.What is the value of 10⁵? =
  24. 24.What is the value of 2⁻⁵ (as a fraction)? =
  25. 25.Write 4.6 × 10⁻² as a decimal. =
  26. 26.Write 38,00,000 in standard form as 3.8 × 10ⁿ. What is n?
  27. 27.What is the value of (1/7)⁻²? =
  28. 28.What is the value of 5¹ × 5⁻⁵? =
  29. 29.What is the value of 3⁸? =
  30. 30.Write 6⁹ ÷ 6⁷ as a single power 6ⁿ. What is n?
  31. 31.Write 4.7 × 10⁻³ as a decimal. =
  32. 32.Write 1,20,000 in standard form as 1.2 × 10ⁿ. What is n?
  33. 33.Write 3.7 × 10⁻³ as a decimal. =
  34. 34.Write 2.5 × 10⁻³ as a decimal. =
  35. 35.2.5 × 10⁴ =
  36. 36.Write 6.9 × 10⁻⁴ as a decimal. =
  37. 37.9 × 10⁵ =
  38. 38.What is the value of 3² × 3⁻⁴? =
  39. 39.Write 9⁴ × 9⁶ as a single power 9ⁿ. What is n?
  40. 40.What is the value of 2⁶ × 2⁻⁴? =

Answer key

  1. 3
  2. 5
  3. 3400
  4. 10
  5. 256
  6. 1/2
  7. 1/7
  8. 10
  9. 14
  10. 6561
  11. 1/256
  12. 625
  13. 1/4
  14. 15625
  15. 12
  16. 15
  17. 13
  18. 1/5
  19. 4/3
  20. 9
  21. 16
  22. 46656
  23. 100000
  24. 1/32
  25. 0.046
  26. 6
  27. 49
  28. 1/625
  29. 6561
  30. 2
  31. 0.0047
  32. 5
  33. 0.0037
  34. 0.0025
  35. 25000
  36. 0.00069
  37. 900000
  38. 1/9
  39. 10
  40. 4

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