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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 731 · 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 790 in standard form as 7.9 × 10ⁿ. What is n?
  2. 2.What is the value of 10⁻³ (as a fraction)? =
  3. 3.Write 4.7 × 10⁻¹ as a decimal. =
  4. 4.Write 38,000 in standard form as 3.8 × 10ⁿ. What is n?
  5. 5.What is the value of 3⁻³ (as a fraction)? =
  6. 6.Write 2¹⁴ ÷ 2⁹ as a single power 2ⁿ. What is n?
  7. 7.6 × 10⁴ =
  8. 8.What is the value of 4⁻³ (as a fraction)? =
  9. 9.What is the value of 5⁶? =
  10. 10.What is the value of 10²? =
  11. 11.Write 21,000 in standard form as 2.1 × 10ⁿ. What is n?
  12. 12.What is the value of 2⁻⁷ (as a fraction)? =
  13. 13.What is the value of 5⁻³ (as a fraction)? =
  14. 14.Write 3.1 × 10⁻¹ as a decimal. =
  15. 15.What is the value of (5/7)⁻²? =
  16. 16.Write 3.4 × 10⁻¹ as a decimal. =
  17. 17.Write 7.9 × 10⁻⁴ as a decimal. =
  18. 18.What is the value of 3⁴ × 3⁻³? =
  19. 19.Write 5⁹ ÷ 5⁴ as a single power 5ⁿ. What is n?
  20. 20.What is the value of 3⁶ × 3⁻³? =
  21. 21.What is the value of 5⁴ × 5⁻³? =
  22. 22.What is the value of 5⁻⁴ (as a fraction)? =
  23. 23.What is the value of (7/9)⁻¹? =
  24. 24.Write 1.9 × 10⁻¹ as a decimal. =
  25. 25.Write (3²)⁷ as a single power 3ⁿ. What is n?
  26. 26.What is the value of 7⁻¹ (as a fraction)? =
  27. 27.What is the value of 10¹ × 10⁻⁴? =
  28. 28.What is the value of 7⁻³ (as a fraction)? =
  29. 29.Write 9.5 × 10⁻³ as a decimal. =
  30. 30.Write (5⁸)⁶ as a single power 5ⁿ. What is n?
  31. 31.What is the value of 8⁵? =
  32. 32.What is the value of 2⁵? =
  33. 33.What is the value of (1/3)⁻²? =
  34. 34.Write 6.2 × 10⁻³ as a decimal. =
  35. 35.Write (2²)⁹ as a single power 2ⁿ. What is n?
  36. 36.What is the value of 9⁻³ (as a fraction)? =
  37. 37.Write 20,000 in standard form as 2 × 10ⁿ. What is n?
  38. 38.Write 970 in standard form as 9.7 × 10ⁿ. What is n?
  39. 39.Write 7.8 × 10⁻¹ as a decimal. =
  40. 40.What is the value of 9⁵? =

Answer key

  1. 2
  2. 1/1000
  3. 0.47
  4. 4
  5. 1/27
  6. 5
  7. 60000
  8. 1/64
  9. 15625
  10. 100
  11. 4
  12. 1/128
  13. 1/125
  14. 0.31
  15. 49/25
  16. 0.34
  17. 0.00079
  18. 3
  19. 5
  20. 27
  21. 5
  22. 1/625
  23. 9/7
  24. 0.19
  25. 14
  26. 1/7
  27. 1/1000
  28. 1/343
  29. 0.0095
  30. 48
  31. 32768
  32. 32
  33. 9
  34. 0.0062
  35. 18
  36. 1/729
  37. 4
  38. 2
  39. 0.78
  40. 59049

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