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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 373 · 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.Write 3,800 in standard form as 3.8 × 10ⁿ. What is n?
  2. 2.What is the value of 5⁷? =
  3. 3.What is the value of 3¹⁰? =
  4. 4.Write 3¹⁷ ÷ 3⁹ as a single power 3ⁿ. What is n?
  5. 5.What is the value of 3²? =
  6. 6.What is the value of 10⁴ × 10⁻³? =
  7. 7.Write 2 × 10⁻² as a decimal. =
  8. 8.Write 7⁷ × 7⁷ as a single power 7ⁿ. What is n?
  9. 9.Write 8.5 × 10⁻² as a decimal. =
  10. 10.9.3 × 10² =
  11. 11.What is the value of 5⁻³ (as a fraction)? =
  12. 12.Write 2,500 in standard form as 2.5 × 10ⁿ. What is n?
  13. 13.Write 1,50,000 in standard form as 1.5 × 10ⁿ. What is n?
  14. 14.What is the value of 5²? =
  15. 15.Write 9.5 × 10⁻⁴ as a decimal. =
  16. 16.Write 310 in standard form as 3.1 × 10ⁿ. What is n?
  17. 17.9.5 × 10² =
  18. 18.What is the value of 4³? =
  19. 19.Write 9⁹ ÷ 9⁴ as a single power 9ⁿ. What is n?
  20. 20.What is the value of 3² × 3⁻²? =
  21. 21.What is the value of 2⁻⁹ (as a fraction)? =
  22. 22.Write 9.9 × 10⁻³ as a decimal. =
  23. 23.Write 1.4 × 10⁻² as a decimal. =
  24. 24.Write 3.2 × 10⁻³ as a decimal. =
  25. 25.Write 2⁵ × 2⁹ as a single power 2ⁿ. What is n?
  26. 26.4.1 × 10³ =
  27. 27.What is the value of 10⁵? =
  28. 28.Write 5⁴ ÷ 5² as a single power 5ⁿ. What is n?
  29. 29.Write 7¹² ÷ 7⁴ as a single power 7ⁿ. What is n?
  30. 30.What is the value of 2² × 2⁻³? =
  31. 31.Write (6⁵)⁸ as a single power 6ⁿ. What is n?
  32. 32.Write 2.8 × 10⁻⁴ as a decimal. =
  33. 33.9.1 × 10⁶ =
  34. 34.What is the value of (4/5)⁻¹? =
  35. 35.Write 7⁵ × 7⁸ as a single power 7ⁿ. What is n?
  36. 36.What is the value of (2/3)⁻²? =
  37. 37.Write 6.9 × 10⁻⁴ as a decimal. =
  38. 38.Write (4⁴)⁷ as a single power 4ⁿ. What is n?
  39. 39.What is the value of 5⁴? =
  40. 40.What is the value of 5⁴ × 5⁻⁶? =

Answer key

  1. 3
  2. 78125
  3. 59049
  4. 8
  5. 9
  6. 10
  7. 0.02
  8. 14
  9. 0.085
  10. 930
  11. 1/125
  12. 3
  13. 5
  14. 25
  15. 0.00095
  16. 2
  17. 950
  18. 64
  19. 5
  20. 1
  21. 1/512
  22. 0.0099
  23. 0.014
  24. 0.0032
  25. 14
  26. 4100
  27. 100000
  28. 2
  29. 8
  30. 1/2
  31. 40
  32. 0.00028
  33. 9100000
  34. 5/4
  35. 13
  36. 9/4
  37. 0.00069
  38. 28
  39. 625
  40. 1/25

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