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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 424 · 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 (3²)⁵ as a single power 3ⁿ. What is n?
  2. 2.Write 9.8 × 10⁻¹ as a decimal. =
  3. 3.Write (5²)⁹ as a single power 5ⁿ. What is n?
  4. 4.What is the value of 6²? =
  5. 5.Write 9.1 × 10⁻⁴ as a decimal. =
  6. 6.Write 3.1 × 10⁻¹ as a decimal. =
  7. 7.What is the value of 2⁻¹ (as a fraction)? =
  8. 8.Write 9,40,000 in standard form as 9.4 × 10ⁿ. What is n?
  9. 9.Write (2⁴)⁶ as a single power 2ⁿ. What is n?
  10. 10.Write 1.1 × 10⁻⁴ as a decimal. =
  11. 11.Write (2⁸)⁷ as a single power 2ⁿ. What is n?
  12. 12.Write 7⁹ × 7² as a single power 7ⁿ. What is n?
  13. 13.What is the value of 3¹⁰? =
  14. 14.Write 3.9 × 10⁻² as a decimal. =
  15. 15.7.5 × 10⁶ =
  16. 16.What is the value of 3⁻¹ (as a fraction)? =
  17. 17.Write 5¹⁰ ÷ 5⁵ as a single power 5ⁿ. What is n?
  18. 18.What is the value of 5³? =
  19. 19.What is the value of 3³ × 3⁻²? =
  20. 20.What is the value of 2² × 2⁻⁴? =
  21. 21.What is the value of (1/3)⁻¹? =
  22. 22.2.3 × 10⁷ =
  23. 23.What is the value of 8⁵? =
  24. 24.3.3 × 10⁴ =
  25. 25.What is the value of 2⁵ × 2⁻¹? =
  26. 26.7.5 × 10³ =
  27. 27.What is the value of 10²? =
  28. 28.4.6 × 10⁵ =
  29. 29.Write 5.1 × 10⁻² as a decimal. =
  30. 30.Write 2.5 × 10⁻² as a decimal. =
  31. 31.Write (9⁷)⁶ as a single power 9ⁿ. What is n?
  32. 32.What is the value of 5⁻² (as a fraction)? =
  33. 33.What is the value of 10² × 10⁻⁵? =
  34. 34.What is the value of 2¹ × 2⁻⁶? =
  35. 35.Write 8⁹ ÷ 8⁵ as a single power 8ⁿ. What is n?
  36. 36.What is the value of 3²? =
  37. 37.What is the value of 8³? =
  38. 38.What is the value of (3/5)⁻²? =
  39. 39.What is the value of 5⁶? =
  40. 40.What is the value of 10⁻¹ (as a fraction)? =

Answer key

  1. 10
  2. 0.98
  3. 18
  4. 36
  5. 0.00091
  6. 0.31
  7. 1/2
  8. 5
  9. 24
  10. 0.00011
  11. 56
  12. 11
  13. 59049
  14. 0.039
  15. 7500000
  16. 1/3
  17. 5
  18. 125
  19. 3
  20. 1/4
  21. 3
  22. 23000000
  23. 32768
  24. 33000
  25. 16
  26. 7500
  27. 100
  28. 460000
  29. 0.051
  30. 0.025
  31. 42
  32. 1/25
  33. 1/1000
  34. 1/32
  35. 4
  36. 9
  37. 512
  38. 25/9
  39. 15625
  40. 1/10

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