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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 342 · 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. 1.6 × 10⁷ =
  2. 2.Write 7⁹ × 7⁷ as a single power 7ⁿ. What is n?
  3. 3.Write 4¹³ ÷ 4⁹ as a single power 4ⁿ. What is n?
  4. 4.What is the value of 2⁶ × 2⁻¹? =
  5. 5.Write 7.4 × 10⁻⁴ as a decimal. =
  6. 6.What is the value of 9⁻¹ (as a fraction)? =
  7. 7.What is the value of 3⁴ × 3⁻⁶? =
  8. 8.Write 86,000 in standard form as 8.6 × 10ⁿ. What is n?
  9. 9.Write 8.7 × 10⁻¹ as a decimal. =
  10. 10.Write 3.8 × 10⁻⁴ as a decimal. =
  11. 11.What is the value of 3⁵ × 3⁻¹? =
  12. 12.Write 9.7 × 10⁻² as a decimal. =
  13. 13.Write 6.1 × 10⁻¹ as a decimal. =
  14. 14.What is the value of 10²? =
  15. 15.Write 1.1 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 10⁻² (as a fraction)? =
  17. 17.What is the value of 8⁴? =
  18. 18.Write 4⁷ × 4⁷ as a single power 4ⁿ. What is n?
  19. 19.What is the value of 2⁻⁶ (as a fraction)? =
  20. 20.What is the value of (2/7)⁻²? =
  21. 21.Write 3.3 × 10⁻³ as a decimal. =
  22. 22.Write 6¹² ÷ 6⁶ as a single power 6ⁿ. What is n?
  23. 23.Write 9⁶ ÷ 9³ as a single power 9ⁿ. What is n?
  24. 24.What is the value of (3/7)⁻²? =
  25. 25.What is the value of (2/5)⁻²? =
  26. 26.What is the value of 3³ × 3⁻¹? =
  27. 27.What is the value of 4⁻¹ (as a fraction)? =
  28. 28.What is the value of 5⁵ × 5⁻¹? =
  29. 29.What is the value of 2⁷? =
  30. 30.What is the value of (1/5)⁻¹? =
  31. 31.Write 9³ × 9² as a single power 9ⁿ. What is n?
  32. 32.3.9 × 10² =
  33. 33.Write 1.4 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 6⁴? =
  35. 35.Write 8.5 × 10⁻³ as a decimal. =
  36. 36.Write 840 in standard form as 8.4 × 10ⁿ. What is n?
  37. 37.What is the value of 2⁵ × 2⁻¹? =
  38. 38.2.4 × 10³ =
  39. 39.Write 7.9 × 10⁻² as a decimal. =
  40. 40.Write 5² × 5⁷ as a single power 5ⁿ. What is n?

Answer key

  1. 60000000
  2. 16
  3. 4
  4. 32
  5. 0.00074
  6. 1/9
  7. 1/9
  8. 4
  9. 0.87
  10. 0.00038
  11. 81
  12. 0.097
  13. 0.61
  14. 100
  15. 0.00011
  16. 1/100
  17. 4096
  18. 14
  19. 1/64
  20. 49/4
  21. 0.0033
  22. 6
  23. 3
  24. 49/9
  25. 25/4
  26. 9
  27. 1/4
  28. 625
  29. 128
  30. 5
  31. 5
  32. 390
  33. 0.14
  34. 1296
  35. 0.0085
  36. 2
  37. 16
  38. 2400
  39. 0.079
  40. 9

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