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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 24 · 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 7¹³ ÷ 7⁵ as a single power 7ⁿ. What is n?
  2. 2.Write 9.5 × 10⁻¹ as a decimal. =
  3. 3.Write (6⁹)⁸ as a single power 6ⁿ. What is n?
  4. 4.Write 2⁸ × 2³ as a single power 2ⁿ. What is n?
  5. 5.Write 6⁴ × 6⁴ as a single power 6ⁿ. What is n?
  6. 6.What is the value of 2³ × 2⁻⁵? =
  7. 7.What is the value of 2⁶? =
  8. 8.What is the value of (2/7)⁻²? =
  9. 9.What is the value of 6⁵? =
  10. 10.Write 6⁵ × 6⁸ as a single power 6ⁿ. What is n?
  11. 11.What is the value of 3⁸? =
  12. 12.Write 8.3 × 10⁻⁴ as a decimal. =
  13. 13.Write 390 in standard form as 3.9 × 10ⁿ. What is n?
  14. 14.What is the value of 6⁻¹ (as a fraction)? =
  15. 15.Write 5.7 × 10⁻¹ as a decimal. =
  16. 16.What is the value of 5⁵ × 5⁻⁴? =
  17. 17.What is the value of 10⁵ × 10⁻⁶? =
  18. 18.Write 9⁸ ÷ 9³ as a single power 9ⁿ. What is n?
  19. 19.Write 2,60,000 in standard form as 2.6 × 10ⁿ. What is n?
  20. 20.What is the value of 6²? =
  21. 21.6.4 × 10³ =
  22. 22.What is the value of (1/3)⁻¹? =
  23. 23.Write 280 in standard form as 2.8 × 10ⁿ. What is n?
  24. 24.Write 2,400 in standard form as 2.4 × 10ⁿ. What is n?
  25. 25.Write (5²)² as a single power 5ⁿ. What is n?
  26. 26.What is the value of 2² × 2⁻¹? =
  27. 27.What is the value of 5² × 5⁻²? =
  28. 28.Write 6,70,000 in standard form as 6.7 × 10ⁿ. What is n?
  29. 29.What is the value of 2¹³? =
  30. 30.Write 6⁵ × 6⁶ as a single power 6ⁿ. What is n?
  31. 31.What is the value of 2⁻² (as a fraction)? =
  32. 32.What is the value of 2²? =
  33. 33.Write 7.3 × 10⁻³ as a decimal. =
  34. 34.What is the value of 8⁻² (as a fraction)? =
  35. 35.What is the value of 3⁹? =
  36. 36.Write 4.2 × 10⁻² as a decimal. =
  37. 37.What is the value of 7⁻¹ (as a fraction)? =
  38. 38.What is the value of 5⁶ × 5⁻¹? =
  39. 39.Write (8⁴)⁶ as a single power 8ⁿ. What is n?
  40. 40.Write (2⁹)⁵ as a single power 2ⁿ. What is n?

Answer key

  1. 8
  2. 0.95
  3. 72
  4. 11
  5. 8
  6. 1/4
  7. 64
  8. 49/4
  9. 7776
  10. 13
  11. 6561
  12. 0.00083
  13. 2
  14. 1/6
  15. 0.57
  16. 5
  17. 1/10
  18. 5
  19. 5
  20. 36
  21. 6400
  22. 3
  23. 2
  24. 3
  25. 4
  26. 2
  27. 1
  28. 5
  29. 8192
  30. 11
  31. 1/4
  32. 4
  33. 0.0073
  34. 1/64
  35. 19683
  36. 0.042
  37. 1/7
  38. 3125
  39. 24
  40. 45

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