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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 917 · 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 9.2 × 10⁻³ as a decimal. =
  2. 2.Write 5.3 × 10⁻³ as a decimal. =
  3. 3.Write 680 in standard form as 6.8 × 10ⁿ. What is n?
  4. 4.What is the value of 3⁻⁵ (as a fraction)? =
  5. 5.What is the value of 3¹ × 3⁻²? =
  6. 6.Write 4.9 × 10⁻³ as a decimal. =
  7. 7.Write 44,000 in standard form as 4.4 × 10ⁿ. What is n?
  8. 8.Write 2.3 × 10⁻¹ as a decimal. =
  9. 9.What is the value of 2² × 2⁻⁵? =
  10. 10.6 × 10⁶ =
  11. 11.What is the value of 7⁴? =
  12. 12.5.1 × 10⁶ =
  13. 13.What is the value of (5/7)⁻²? =
  14. 14.What is the value of 2⁻³ (as a fraction)? =
  15. 15.Write 8⁹ × 8³ as a single power 8ⁿ. What is n?
  16. 16.Write 1.5 × 10⁻² as a decimal. =
  17. 17.What is the value of (3/4)⁻¹? =
  18. 18.Write (3⁵)⁵ as a single power 3ⁿ. What is n?
  19. 19.Write 1,700 in standard form as 1.7 × 10ⁿ. What is n?
  20. 20.Write 5⁵ × 5⁴ as a single power 5ⁿ. What is n?
  21. 21.Write 54,00,000 in standard form as 5.4 × 10ⁿ. What is n?
  22. 22.What is the value of 3⁻² (as a fraction)? =
  23. 23.What is the value of 6⁻³ (as a fraction)? =
  24. 24.Write (4⁵)⁴ as a single power 4ⁿ. What is n?
  25. 25.What is the value of 2¹⁴? =
  26. 26.What is the value of 7⁵? =
  27. 27.What is the value of 2² × 2⁻¹? =
  28. 28.What is the value of 3⁶ × 3⁻⁵? =
  29. 29.Write (5²)⁹ as a single power 5ⁿ. What is n?
  30. 30.Write (5⁶)⁷ as a single power 5ⁿ. What is n?
  31. 31.What is the value of 3⁷? =
  32. 32.What is the value of 6⁵? =
  33. 33.What is the value of 3⁴ × 3⁻⁴? =
  34. 34.Write 9⁵ × 9⁷ as a single power 9ⁿ. What is n?
  35. 35.What is the value of 5⁷? =
  36. 36.What is the value of 3⁹? =
  37. 37.Write 2¹⁵ ÷ 2⁷ as a single power 2ⁿ. What is n?
  38. 38.Write 4⁶ × 4⁸ as a single power 4ⁿ. What is n?
  39. 39.What is the value of 3¹ × 3⁻⁵? =
  40. 40.Write 4.2 × 10⁻³ as a decimal. =

Answer key

  1. 0.0092
  2. 0.0053
  3. 2
  4. 1/243
  5. 1/3
  6. 0.0049
  7. 4
  8. 0.23
  9. 1/8
  10. 6000000
  11. 2401
  12. 5100000
  13. 49/25
  14. 1/8
  15. 12
  16. 0.015
  17. 4/3
  18. 25
  19. 3
  20. 9
  21. 6
  22. 1/9
  23. 1/216
  24. 20
  25. 16384
  26. 16807
  27. 2
  28. 3
  29. 18
  30. 42
  31. 2187
  32. 7776
  33. 1
  34. 12
  35. 78125
  36. 19683
  37. 8
  38. 14
  39. 1/81
  40. 0.0042

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