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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 400 · 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 5.4 × 10⁻² as a decimal. =
  2. 2.What is the value of 10⁴ × 10⁻⁵? =
  3. 3.Write 4.3 × 10⁻³ as a decimal. =
  4. 4.Write 2⁵ × 2⁸ as a single power 2ⁿ. What is n?
  5. 5.What is the value of 5⁻³ (as a fraction)? =
  6. 6.What is the value of (2/9)⁻¹? =
  7. 7.What is the value of 5¹ × 5⁻⁴? =
  8. 8.What is the value of 2⁶ × 2⁻¹? =
  9. 9.What is the value of (5/9)⁻²? =
  10. 10.What is the value of 2¹⁴? =
  11. 11.What is the value of 5⁵ × 5⁻¹? =
  12. 12.Write 7⁹ × 7³ as a single power 7ⁿ. What is n?
  13. 13.2.4 × 10⁶ =
  14. 14.What is the value of 2⁻⁸ (as a fraction)? =
  15. 15.Write 9⁷ × 9⁵ as a single power 9ⁿ. What is n?
  16. 16.Write (9⁴)³ as a single power 9ⁿ. What is n?
  17. 17.9.4 × 10⁵ =
  18. 18.What is the value of 5⁵ × 5⁻²? =
  19. 19.Write 8,500 in standard form as 8.5 × 10ⁿ. What is n?
  20. 20.What is the value of 3²? =
  21. 21.What is the value of 2⁶? =
  22. 22.What is the value of 6⁴? =
  23. 23.Write 3.3 × 10⁻³ as a decimal. =
  24. 24.What is the value of 2¹⁶? =
  25. 25.Write 4⁸ × 4³ as a single power 4ⁿ. What is n?
  26. 26.Write 450 in standard form as 4.5 × 10ⁿ. What is n?
  27. 27.What is the value of (1/8)⁻¹? =
  28. 28.What is the value of 4²? =
  29. 29.Write 6.2 × 10⁻³ as a decimal. =
  30. 30.Write 6.1 × 10⁻³ as a decimal. =
  31. 31.What is the value of 10⁶ × 10⁻³? =
  32. 32.What is the value of 2⁹? =
  33. 33.Write (8²)⁷ as a single power 8ⁿ. What is n?
  34. 34.Write 7² × 7⁴ as a single power 7ⁿ. What is n?
  35. 35.What is the value of (3/7)⁻²? =
  36. 36.What is the value of (3/8)⁻²? =
  37. 37.3.1 × 10³ =
  38. 38.Write 2¹⁴ ÷ 2⁵ as a single power 2ⁿ. What is n?
  39. 39.Write 4.1 × 10⁻² as a decimal. =
  40. 40.Write 8¹⁶ ÷ 8⁷ as a single power 8ⁿ. What is n?

Answer key

  1. 0.054
  2. 1/10
  3. 0.0043
  4. 13
  5. 1/125
  6. 9/2
  7. 1/125
  8. 32
  9. 81/25
  10. 16384
  11. 625
  12. 12
  13. 2400000
  14. 1/256
  15. 12
  16. 12
  17. 940000
  18. 125
  19. 3
  20. 9
  21. 64
  22. 1296
  23. 0.0033
  24. 65536
  25. 11
  26. 2
  27. 8
  28. 16
  29. 0.0062
  30. 0.0061
  31. 1000
  32. 512
  33. 14
  34. 6
  35. 49/9
  36. 64/9
  37. 3100
  38. 9
  39. 0.041
  40. 9

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