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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 852 · 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 (3³)⁶ as a single power 3ⁿ. What is n?
  2. 2.Write 4⁷ × 4⁹ as a single power 4ⁿ. What is n?
  3. 3.Write 6⁴ × 6⁶ as a single power 6ⁿ. What is n?
  4. 4.Write (3⁷)⁹ as a single power 3ⁿ. What is n?
  5. 5.Write 24,000 in standard form as 2.4 × 10ⁿ. What is n?
  6. 6.What is the value of 4⁷? =
  7. 7.Write 5.6 × 10⁻¹ as a decimal. =
  8. 8.9.1 × 10² =
  9. 9.Write 620 in standard form as 6.2 × 10ⁿ. What is n?
  10. 10.Write 4⁷ × 4⁶ as a single power 4ⁿ. What is n?
  11. 11.6.3 × 10³ =
  12. 12.What is the value of 2⁶ × 2⁻⁴? =
  13. 13.What is the value of 4⁻⁴ (as a fraction)? =
  14. 14.Write 7.1 × 10⁻³ as a decimal. =
  15. 15.Write 2.9 × 10⁻² as a decimal. =
  16. 16.Write 1.8 × 10⁻¹ as a decimal. =
  17. 17.What is the value of 2⁻⁸ (as a fraction)? =
  18. 18.What is the value of 9⁻³ (as a fraction)? =
  19. 19.Write 6¹⁰ ÷ 6⁵ as a single power 6ⁿ. What is n?
  20. 20.What is the value of 5⁴ × 5⁻¹? =
  21. 21.What is the value of 10⁴ × 10⁻⁴? =
  22. 22.Write 4¹² ÷ 4³ as a single power 4ⁿ. What is n?
  23. 23.What is the value of (2/3)⁻²? =
  24. 24.2.9 × 10² =
  25. 25.Write 6³ × 6⁶ as a single power 6ⁿ. What is n?
  26. 26.Write 360 in standard form as 3.6 × 10ⁿ. What is n?
  27. 27.What is the value of 8³? =
  28. 28.What is the value of 2¹ × 2⁻³? =
  29. 29.Write 4.7 × 10⁻² as a decimal. =
  30. 30.What is the value of (4/7)⁻²? =
  31. 31.What is the value of (7/9)⁻²? =
  32. 32.Write 510 in standard form as 5.1 × 10ⁿ. What is n?
  33. 33.What is the value of 4⁸? =
  34. 34.What is the value of 5³? =
  35. 35.Write 3⁴ ÷ 3² as a single power 3ⁿ. What is n?
  36. 36.Write 49,00,000 in standard form as 4.9 × 10ⁿ. What is n?
  37. 37.What is the value of 9³? =
  38. 38.What is the value of 2⁷? =
  39. 39.What is the value of 2¹⁶? =
  40. 40.What is the value of (7/8)⁻¹? =

Answer key

  1. 18
  2. 16
  3. 10
  4. 63
  5. 4
  6. 16384
  7. 0.56
  8. 910
  9. 2
  10. 13
  11. 6300
  12. 4
  13. 1/256
  14. 0.0071
  15. 0.029
  16. 0.18
  17. 1/256
  18. 1/729
  19. 5
  20. 125
  21. 1
  22. 9
  23. 9/4
  24. 290
  25. 9
  26. 2
  27. 512
  28. 1/4
  29. 0.047
  30. 49/16
  31. 81/49
  32. 2
  33. 65536
  34. 125
  35. 2
  36. 6
  37. 729
  38. 128
  39. 65536
  40. 8/7

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