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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 123 · 40 sums
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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. 1.6.5 × 10⁴ =
  2. 2.3.7 × 10⁴ =
  3. 3.Write 1.6 × 10⁻³ as a decimal. =
  4. 4.What is the value of 5⁵ × 5⁻³? =
  5. 5.What is the value of 5¹ × 5⁻²? =
  6. 6.Write (3²)⁷ as a single power 3ⁿ. What is n?
  7. 7.Write 4⁴ × 4² as a single power 4ⁿ. What is n?
  8. 8.Write 3.3 × 10⁻¹ as a decimal. =
  9. 9.Write 72,000 in standard form as 7.2 × 10ⁿ. What is n?
  10. 10.Write (5⁴)² as a single power 5ⁿ. What is n?
  11. 11.What is the value of 10² × 10⁻⁵? =
  12. 12.Write 8⁶ ÷ 8² as a single power 8ⁿ. What is n?
  13. 13.What is the value of 3⁴? =
  14. 14.9.7 × 10⁵ =
  15. 15.Write 7⁷ × 7⁴ as a single power 7ⁿ. What is n?
  16. 16.Write 5.9 × 10⁻¹ as a decimal. =
  17. 17.What is the value of (3/8)⁻²? =
  18. 18.What is the value of (2/5)⁻²? =
  19. 19.What is the value of 2⁵ × 2⁻⁶? =
  20. 20.Write (2⁹)⁴ as a single power 2ⁿ. What is n?
  21. 21.What is the value of 10⁻³ (as a fraction)? =
  22. 22.What is the value of 5⁶? =
  23. 23.Write 9⁸ × 9⁵ as a single power 9ⁿ. What is n?
  24. 24.What is the value of (4/7)⁻¹? =
  25. 25.Write 2.5 × 10⁻³ as a decimal. =
  26. 26.Write 300 in standard form as 3 × 10ⁿ. What is n?
  27. 27.What is the value of 2¹⁴? =
  28. 28.Write 3.6 × 10⁻³ as a decimal. =
  29. 29.What is the value of 2¹⁰? =
  30. 30.What is the value of 2³ × 2⁻⁶? =
  31. 31.What is the value of 5⁵? =
  32. 32.Write 8 × 10⁻³ as a decimal. =
  33. 33.Write 7,40,00,000 in standard form as 7.4 × 10ⁿ. What is n?
  34. 34.Write 460 in standard form as 4.6 × 10ⁿ. What is n?
  35. 35.What is the value of 6⁻¹ (as a fraction)? =
  36. 36.Write 740 in standard form as 7.4 × 10ⁿ. What is n?
  37. 37.7.8 × 10⁴ =
  38. 38.What is the value of 2⁷? =
  39. 39.Write 9.4 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of 6⁴? =

Answer key

  1. 65000
  2. 37000
  3. 0.0016
  4. 25
  5. 1/5
  6. 14
  7. 6
  8. 0.33
  9. 4
  10. 8
  11. 1/1000
  12. 4
  13. 81
  14. 970000
  15. 11
  16. 0.59
  17. 64/9
  18. 25/4
  19. 1/2
  20. 36
  21. 1/1000
  22. 15625
  23. 13
  24. 7/4
  25. 0.0025
  26. 2
  27. 16384
  28. 0.0036
  29. 1024
  30. 1/8
  31. 3125
  32. 0.008
  33. 7
  34. 2
  35. 1/6
  36. 2
  37. 78000
  38. 128
  39. 0.00094
  40. 1296

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