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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 209 · 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.What is the value of 10¹ × 10⁻⁵? =
  2. 2.What is the value of 5⁶? =
  3. 3.What is the value of 7⁴? =
  4. 4.What is the value of 4⁻² (as a fraction)? =
  5. 5.Write 1,700 in standard form as 1.7 × 10ⁿ. What is n?
  6. 6.What is the value of 6⁻³ (as a fraction)? =
  7. 7.What is the value of 3⁵ × 3⁻²? =
  8. 8.What is the value of 7⁻² (as a fraction)? =
  9. 9.What is the value of 3³ × 3⁻⁵? =
  10. 10.3.7 × 10⁵ =
  11. 11.What is the value of 3⁻³ (as a fraction)? =
  12. 12.Write 8¹² ÷ 8⁸ as a single power 8ⁿ. What is n?
  13. 13.What is the value of 4⁻³ (as a fraction)? =
  14. 14.What is the value of (1/3)⁻¹? =
  15. 15.7.3 × 10⁶ =
  16. 16.What is the value of 2² × 2⁻³? =
  17. 17.What is the value of 7⁻¹ (as a fraction)? =
  18. 18.What is the value of 9⁵? =
  19. 19.What is the value of 5³ × 5⁻³? =
  20. 20.What is the value of 6⁶? =
  21. 21.What is the value of 5⁷? =
  22. 22.What is the value of 9³? =
  23. 23.Write 4⁹ × 4⁷ as a single power 4ⁿ. What is n?
  24. 24.6.3 × 10⁷ =
  25. 25.Write 6.8 × 10⁻⁴ as a decimal. =
  26. 26.What is the value of 6⁵? =
  27. 27.What is the value of 2² × 2⁻⁵? =
  28. 28.6.1 × 10² =
  29. 29.What is the value of (3/5)⁻²? =
  30. 30.What is the value of 2⁶? =
  31. 31.What is the value of 3¹ × 3⁻¹? =
  32. 32.Write 1,300 in standard form as 1.3 × 10ⁿ. What is n?
  33. 33.Write 41,000 in standard form as 4.1 × 10ⁿ. What is n?
  34. 34.Write 94,00,000 in standard form as 9.4 × 10ⁿ. What is n?
  35. 35.What is the value of 2¹⁶? =
  36. 36.Write 3² × 3² as a single power 3ⁿ. What is n?
  37. 37.Write 3¹³ ÷ 3⁹ as a single power 3ⁿ. What is n?
  38. 38.What is the value of (7/8)⁻²? =
  39. 39.What is the value of 2⁵? =
  40. 40.What is the value of 10³ × 10⁻³? =

Answer key

  1. 1/10000
  2. 15625
  3. 2401
  4. 1/16
  5. 3
  6. 1/216
  7. 27
  8. 1/49
  9. 1/9
  10. 370000
  11. 1/27
  12. 4
  13. 1/64
  14. 3
  15. 7300000
  16. 1/2
  17. 1/7
  18. 59049
  19. 1
  20. 46656
  21. 78125
  22. 729
  23. 16
  24. 63000000
  25. 0.00068
  26. 7776
  27. 1/8
  28. 610
  29. 25/9
  30. 64
  31. 1
  32. 3
  33. 4
  34. 6
  35. 65536
  36. 4
  37. 4
  38. 64/49
  39. 32
  40. 1

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