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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 654 · 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 7⁻³ (as a fraction)? =
  2. 2.What is the value of 2¹⁴? =
  3. 3.Write 6⁸ × 6⁹ as a single power 6ⁿ. What is n?
  4. 4.What is the value of 2¹³? =
  5. 5.Write 2⁴ × 2⁴ as a single power 2ⁿ. What is n?
  6. 6.Write 6³ × 6⁸ as a single power 6ⁿ. What is n?
  7. 7.What is the value of 10⁻² (as a fraction)? =
  8. 8.Write 7⁹ ÷ 7⁷ as a single power 7ⁿ. What is n?
  9. 9.What is the value of 4⁻⁴ (as a fraction)? =
  10. 10.Write 7.4 × 10⁻⁴ as a decimal. =
  11. 11.Write (5⁹)⁴ as a single power 5ⁿ. What is n?
  12. 12.What is the value of 6⁶? =
  13. 13.What is the value of 2⁻⁹ (as a fraction)? =
  14. 14.9.5 × 10² =
  15. 15.Write 7.6 × 10⁻¹ as a decimal. =
  16. 16.9.2 × 10⁴ =
  17. 17.Write 7.8 × 10⁻² as a decimal. =
  18. 18.Write 9³ × 9⁹ as a single power 9ⁿ. What is n?
  19. 19.What is the value of (7/9)⁻¹? =
  20. 20.Write (5²)⁵ as a single power 5ⁿ. What is n?
  21. 21.Write 3.5 × 10⁻⁴ as a decimal. =
  22. 22.Write 380 in standard form as 3.8 × 10ⁿ. What is n?
  23. 23.Write 9.7 × 10⁻¹ as a decimal. =
  24. 24.Write 340 in standard form as 3.4 × 10ⁿ. What is n?
  25. 25.5.9 × 10³ =
  26. 26.What is the value of 2² × 2⁻²? =
  27. 27.What is the value of 2⁴? =
  28. 28.Write 6.3 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 3³? =
  30. 30.Write 5⁷ × 5² as a single power 5ⁿ. What is n?
  31. 31.Write 3⁹ ÷ 3³ as a single power 3ⁿ. What is n?
  32. 32.Write 4⁹ × 4⁶ as a single power 4ⁿ. What is n?
  33. 33.Write 120 in standard form as 1.2 × 10ⁿ. What is n?
  34. 34.What is the value of 3⁵? =
  35. 35.Write 5.2 × 10⁻⁴ as a decimal. =
  36. 36.What is the value of (3/4)⁻¹? =
  37. 37.Write 5⁶ × 5⁷ as a single power 5ⁿ. What is n?
  38. 38.Write 4⁶ × 4⁵ as a single power 4ⁿ. What is n?
  39. 39.What is the value of 2⁷? =
  40. 40.What is the value of (5/8)⁻¹? =

Answer key

  1. 1/343
  2. 16384
  3. 17
  4. 8192
  5. 8
  6. 11
  7. 1/100
  8. 2
  9. 1/256
  10. 0.00074
  11. 36
  12. 46656
  13. 1/512
  14. 950
  15. 0.76
  16. 92000
  17. 0.078
  18. 12
  19. 9/7
  20. 10
  21. 0.00035
  22. 2
  23. 0.97
  24. 2
  25. 5900
  26. 1
  27. 16
  28. 0.63
  29. 27
  30. 9
  31. 6
  32. 15
  33. 2
  34. 243
  35. 0.00052
  36. 4/3
  37. 13
  38. 11
  39. 128
  40. 8/5

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