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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 547 · 40 sums
TalentJR

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 7.5 × 10⁻² as a decimal. =
  2. 2.What is the value of 10⁵? =
  3. 3.What is the value of 3² × 3⁻²? =
  4. 4.Write (9⁶)⁸ as a single power 9ⁿ. What is n?
  5. 5.What is the value of 10³ × 10⁻²? =
  6. 6.What is the value of 5⁵? =
  7. 7.Write 2⁸ × 2⁸ as a single power 2ⁿ. What is n?
  8. 8.3.1 × 10² =
  9. 9.What is the value of 2⁵? =
  10. 10.Write 2³ × 2⁴ as a single power 2ⁿ. What is n?
  11. 11.Write 270 in standard form as 2.7 × 10ⁿ. What is n?
  12. 12.Write 6⁵ × 6³ as a single power 6ⁿ. What is n?
  13. 13.Write 22,000 in standard form as 2.2 × 10ⁿ. What is n?
  14. 14.Write 2.2 × 10⁻² as a decimal. =
  15. 15.What is the value of 8³? =
  16. 16.What is the value of 8⁻³ (as a fraction)? =
  17. 17.What is the value of 3² × 3⁻¹? =
  18. 18.What is the value of 3² × 3⁻⁶? =
  19. 19.What is the value of 2¹ × 2⁻¹? =
  20. 20.What is the value of 3⁵? =
  21. 21.What is the value of 3⁸? =
  22. 22.What is the value of 2² × 2⁻²? =
  23. 23.Write (3⁸)² as a single power 3ⁿ. What is n?
  24. 24.What is the value of 5³ × 5⁻⁴? =
  25. 25.What is the value of 2¹¹? =
  26. 26.Write 6⁹ × 6² as a single power 6ⁿ. What is n?
  27. 27.What is the value of 6²? =
  28. 28.Write (4⁴)² as a single power 4ⁿ. What is n?
  29. 29.Write 9⁶ × 9⁷ as a single power 9ⁿ. What is n?
  30. 30.What is the value of 10⁻¹ (as a fraction)? =
  31. 31.What is the value of 2⁵ × 2⁻⁵? =
  32. 32.What is the value of 3⁻³ (as a fraction)? =
  33. 33.Write 1.6 × 10⁻¹ as a decimal. =
  34. 34.Write 440 in standard form as 4.4 × 10ⁿ. What is n?
  35. 35.Write 600 in standard form as 6 × 10ⁿ. What is n?
  36. 36.Write 8¹⁰ ÷ 8⁶ as a single power 8ⁿ. What is n?
  37. 37.Write 7.5 × 10⁻³ as a decimal. =
  38. 38.Write 21,00,000 in standard form as 2.1 × 10ⁿ. What is n?
  39. 39.3.4 × 10³ =
  40. 40.What is the value of 5¹ × 5⁻³? =

Answer key

  1. 0.075
  2. 100000
  3. 1
  4. 48
  5. 10
  6. 3125
  7. 16
  8. 310
  9. 32
  10. 7
  11. 2
  12. 8
  13. 4
  14. 0.022
  15. 512
  16. 1/512
  17. 3
  18. 1/81
  19. 1
  20. 243
  21. 6561
  22. 1
  23. 16
  24. 1/5
  25. 2048
  26. 11
  27. 36
  28. 8
  29. 13
  30. 1/10
  31. 1
  32. 1/27
  33. 0.16
  34. 2
  35. 2
  36. 4
  37. 0.0075
  38. 6
  39. 3400
  40. 1/25

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