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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 595 · 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 3,300 in standard form as 3.3 × 10ⁿ. What is n?
  2. 2.Write 7³ × 7³ as a single power 7ⁿ. What is n?
  3. 3.9.9 × 10³ =
  4. 4.Write 6.2 × 10⁻³ as a decimal. =
  5. 5.Write (8⁵)⁷ as a single power 8ⁿ. What is n?
  6. 6.Write 7.2 × 10⁻³ as a decimal. =
  7. 7.Write 4⁹ × 4² as a single power 4ⁿ. What is n?
  8. 8.Write (5²)⁴ as a single power 5ⁿ. What is n?
  9. 9.What is the value of 2¹ × 2⁻¹? =
  10. 10.What is the value of (5/7)⁻²? =
  11. 11.Write 2,90,000 in standard form as 2.9 × 10ⁿ. What is n?
  12. 12.What is the value of 5² × 5⁻³? =
  13. 13.What is the value of (6/7)⁻²? =
  14. 14.Write 66,000 in standard form as 6.6 × 10ⁿ. What is n?
  15. 15.What is the value of 10¹ × 10⁻²? =
  16. 16.3.5 × 10² =
  17. 17.What is the value of 2¹²? =
  18. 18.What is the value of 3⁶ × 3⁻²? =
  19. 19.Write 6.6 × 10⁻⁴ as a decimal. =
  20. 20.What is the value of 2⁵ × 2⁻⁵? =
  21. 21.Write 9.4 × 10⁻² as a decimal. =
  22. 22.What is the value of 9⁴? =
  23. 23.Write 7.3 × 10⁻¹ as a decimal. =
  24. 24.Write 7.8 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 4⁻³ (as a fraction)? =
  26. 26.What is the value of 2⁻⁸ (as a fraction)? =
  27. 27.Write (3⁸)² as a single power 3ⁿ. What is n?
  28. 28.What is the value of 10²? =
  29. 29.What is the value of (2/5)⁻²? =
  30. 30.Write (7⁴)⁶ as a single power 7ⁿ. What is n?
  31. 31.Write 3.7 × 10⁻⁴ as a decimal. =
  32. 32.What is the value of 5² × 5⁻¹? =
  33. 33.What is the value of 5⁶ × 5⁻²? =
  34. 34.9.1 × 10² =
  35. 35.What is the value of 2¹⁴? =
  36. 36.What is the value of 10⁴ × 10⁻³? =
  37. 37.What is the value of 7³? =
  38. 38.Write 2⁹ ÷ 2² as a single power 2ⁿ. What is n?
  39. 39.What is the value of 2¹¹? =
  40. 40.Write 2,600 in standard form as 2.6 × 10ⁿ. What is n?

Answer key

  1. 3
  2. 6
  3. 9900
  4. 0.0062
  5. 35
  6. 0.0072
  7. 11
  8. 8
  9. 1
  10. 49/25
  11. 5
  12. 1/5
  13. 49/36
  14. 4
  15. 1/10
  16. 350
  17. 4096
  18. 81
  19. 0.00066
  20. 1
  21. 0.094
  22. 6561
  23. 0.73
  24. 0.78
  25. 1/64
  26. 1/256
  27. 16
  28. 100
  29. 25/4
  30. 24
  31. 0.00037
  32. 5
  33. 625
  34. 910
  35. 16384
  36. 10
  37. 343
  38. 7
  39. 2048
  40. 3

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