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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 398 · 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 4.3 × 10⁻¹ as a decimal. =
  2. 2.What is the value of 10¹ × 10⁻¹? =
  3. 3.1.5 × 10³ =
  4. 4.What is the value of 3⁴? =
  5. 5.Write 9¹³ ÷ 9⁹ as a single power 9ⁿ. What is n?
  6. 6.Write 2⁶ × 2⁶ as a single power 2ⁿ. What is n?
  7. 7.What is the value of 2⁴ × 2⁻⁶? =
  8. 8.What is the value of 7⁴? =
  9. 9.What is the value of 5¹ × 5⁻²? =
  10. 10.What is the value of 5² × 5⁻⁴? =
  11. 11.What is the value of 3⁶ × 3⁻⁶? =
  12. 12.What is the value of 6⁴? =
  13. 13.Write (4⁵)⁷ as a single power 4ⁿ. What is n?
  14. 14.What is the value of 10³ × 10⁻⁶? =
  15. 15.Write 9⁹ ÷ 9⁶ as a single power 9ⁿ. What is n?
  16. 16.Write 6.8 × 10⁻⁴ as a decimal. =
  17. 17.What is the value of 4³? =
  18. 18.Write 2⁶ × 2⁷ as a single power 2ⁿ. What is n?
  19. 19.What is the value of 10³ × 10⁻³? =
  20. 20.What is the value of 10² × 10⁻⁴? =
  21. 21.What is the value of 2² × 2⁻¹? =
  22. 22.Write 1.7 × 10⁻² as a decimal. =
  23. 23.What is the value of 2⁻¹ (as a fraction)? =
  24. 24.Write 9,000 in standard form as 9 × 10ⁿ. What is n?
  25. 25.Write (4⁴)⁶ as a single power 4ⁿ. What is n?
  26. 26.Write 5⁸ ÷ 5⁶ as a single power 5ⁿ. What is n?
  27. 27.What is the value of 3³ × 3⁻⁴? =
  28. 28.Write 4¹⁸ ÷ 4⁹ as a single power 4ⁿ. What is n?
  29. 29.Write 4³ × 4⁶ as a single power 4ⁿ. What is n?
  30. 30.Write (9⁴)⁵ as a single power 9ⁿ. What is n?
  31. 31.What is the value of (1/4)⁻¹? =
  32. 32.Write (9³)⁸ as a single power 9ⁿ. What is n?
  33. 33.Write 2.3 × 10⁻¹ as a decimal. =
  34. 34.Write 1.4 × 10⁻¹ as a decimal. =
  35. 35.What is the value of (1/2)⁻²? =
  36. 36.Write 1.2 × 10⁻³ as a decimal. =
  37. 37.Write 5.4 × 10⁻⁴ as a decimal. =
  38. 38.What is the value of 5² × 5⁻³? =
  39. 39.Write (8⁴)⁶ as a single power 8ⁿ. What is n?
  40. 40.What is the value of 5⁶ × 5⁻³? =

Answer key

  1. 0.43
  2. 1
  3. 1500
  4. 81
  5. 4
  6. 12
  7. 1/4
  8. 2401
  9. 1/5
  10. 1/25
  11. 1
  12. 1296
  13. 35
  14. 1/1000
  15. 3
  16. 0.00068
  17. 64
  18. 13
  19. 1
  20. 1/100
  21. 2
  22. 0.017
  23. 1/2
  24. 3
  25. 24
  26. 2
  27. 1/3
  28. 9
  29. 9
  30. 20
  31. 4
  32. 24
  33. 0.23
  34. 0.14
  35. 4
  36. 0.0012
  37. 0.00054
  38. 1/5
  39. 24
  40. 125

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