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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 787 · 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 (4⁵)⁹ as a single power 4ⁿ. What is n?
  2. 2.What is the value of 5⁻³ (as a fraction)? =
  3. 3.What is the value of 2²? =
  4. 4.What is the value of 5⁶ × 5⁻²? =
  5. 5.What is the value of 5⁶ × 5⁻⁴? =
  6. 6.Write 6.1 × 10⁻¹ as a decimal. =
  7. 7.Write 4.5 × 10⁻² as a decimal. =
  8. 8.What is the value of 2¹⁴? =
  9. 9.Write 1.2 × 10⁻² as a decimal. =
  10. 10.Write (8³)⁹ as a single power 8ⁿ. What is n?
  11. 11.What is the value of 3² × 3⁻⁶? =
  12. 12.Write (3⁹)³ as a single power 3ⁿ. What is n?
  13. 13.What is the value of (1/8)⁻²? =
  14. 14.Write 4,800 in standard form as 4.8 × 10ⁿ. What is n?
  15. 15.What is the value of 2⁻⁹ (as a fraction)? =
  16. 16.Write 8.6 × 10⁻⁴ as a decimal. =
  17. 17.Write 68,000 in standard form as 6.8 × 10ⁿ. What is n?
  18. 18.What is the value of 4⁻⁴ (as a fraction)? =
  19. 19.What is the value of 2⁴? =
  20. 20.Write 6⁹ ÷ 6⁶ as a single power 6ⁿ. What is n?
  21. 21.What is the value of 2¹⁶? =
  22. 22.1.6 × 10⁵ =
  23. 23.Write 8⁸ ÷ 8⁶ as a single power 8ⁿ. What is n?
  24. 24.What is the value of 4⁴? =
  25. 25.Write 8¹⁵ ÷ 8⁶ as a single power 8ⁿ. What is n?
  26. 26.Write 4.4 × 10⁻⁴ as a decimal. =
  27. 27.Write 8.2 × 10⁻⁴ as a decimal. =
  28. 28.Write 1.8 × 10⁻¹ as a decimal. =
  29. 29.Write 8⁹ ÷ 8² as a single power 8ⁿ. What is n?
  30. 30.Write 7.2 × 10⁻³ as a decimal. =
  31. 31.What is the value of 10¹ × 10⁻⁶? =
  32. 32.What is the value of 3² × 3⁻⁵? =
  33. 33.What is the value of 7²? =
  34. 34.What is the value of (7/9)⁻²? =
  35. 35.Write 7¹⁰ ÷ 7⁵ as a single power 7ⁿ. What is n?
  36. 36.3.8 × 10⁴ =
  37. 37.What is the value of 6³? =
  38. 38.8.1 × 10³ =
  39. 39.Write 6.8 × 10⁻³ as a decimal. =
  40. 40.Write (7²)⁹ as a single power 7ⁿ. What is n?

Answer key

  1. 45
  2. 1/125
  3. 4
  4. 625
  5. 25
  6. 0.61
  7. 0.045
  8. 16384
  9. 0.012
  10. 27
  11. 1/81
  12. 27
  13. 64
  14. 3
  15. 1/512
  16. 0.00086
  17. 4
  18. 1/256
  19. 16
  20. 3
  21. 65536
  22. 160000
  23. 2
  24. 256
  25. 9
  26. 0.00044
  27. 0.00082
  28. 0.18
  29. 7
  30. 0.0072
  31. 1/100000
  32. 1/27
  33. 49
  34. 81/49
  35. 5
  36. 38000
  37. 216
  38. 8100
  39. 0.0068
  40. 18

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