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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 508 · 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 870 in standard form as 8.7 × 10ⁿ. What is n?
  2. 2.Write 8.4 × 10⁻² as a decimal. =
  3. 3.What is the value of (1/7)⁻²? =
  4. 4.What is the value of 3⁵ × 3⁻⁶? =
  5. 5.What is the value of 9⁻¹ (as a fraction)? =
  6. 6.What is the value of 2⁻³ (as a fraction)? =
  7. 7.What is the value of 2⁶? =
  8. 8.Write 9⁶ × 9⁴ as a single power 9ⁿ. What is n?
  9. 9.Write 7³ × 7⁶ as a single power 7ⁿ. What is n?
  10. 10.1.4 × 10⁴ =
  11. 11.What is the value of 10² × 10⁻⁴? =
  12. 12.Write 5¹⁰ ÷ 5⁶ as a single power 5ⁿ. What is n?
  13. 13.What is the value of 2⁷? =
  14. 14.What is the value of (5/8)⁻²? =
  15. 15.Write (4⁸)⁶ as a single power 4ⁿ. What is n?
  16. 16.What is the value of 5⁵? =
  17. 17.Write (2²)⁹ as a single power 2ⁿ. What is n?
  18. 18.Write 8.2 × 10⁻² as a decimal. =
  19. 19.What is the value of 2⁻⁸ (as a fraction)? =
  20. 20.What is the value of 5⁵ × 5⁻³? =
  21. 21.What is the value of 5¹ × 5⁻⁵? =
  22. 22.What is the value of (5/9)⁻¹? =
  23. 23.What is the value of 10²? =
  24. 24.What is the value of (3/8)⁻²? =
  25. 25.Write 7.2 × 10⁻² as a decimal. =
  26. 26.What is the value of 2¹⁵? =
  27. 27.Write 2.2 × 10⁻¹ as a decimal. =
  28. 28.What is the value of 5⁵ × 5⁻⁵? =
  29. 29.What is the value of 4⁻¹ (as a fraction)? =
  30. 30.What is the value of 4⁸? =
  31. 31.8.8 × 10⁶ =
  32. 32.Write (4²)³ as a single power 4ⁿ. What is n?
  33. 33.What is the value of 2⁶ × 2⁻²? =
  34. 34.What is the value of 10⁻³ (as a fraction)? =
  35. 35.What is the value of (1/8)⁻²? =
  36. 36.Write 6.8 × 10⁻⁴ as a decimal. =
  37. 37.Write 3.8 × 10⁻³ as a decimal. =
  38. 38.Write 1.2 × 10⁻⁴ as a decimal. =
  39. 39.What is the value of 3⁶? =
  40. 40.Write 5² × 5⁷ as a single power 5ⁿ. What is n?

Answer key

  1. 2
  2. 0.084
  3. 49
  4. 1/3
  5. 1/9
  6. 1/8
  7. 64
  8. 10
  9. 9
  10. 14000
  11. 1/100
  12. 4
  13. 128
  14. 64/25
  15. 48
  16. 3125
  17. 18
  18. 0.082
  19. 1/256
  20. 25
  21. 1/625
  22. 9/5
  23. 100
  24. 64/9
  25. 0.072
  26. 32768
  27. 0.22
  28. 1
  29. 1/4
  30. 65536
  31. 8800000
  32. 6
  33. 16
  34. 1/1000
  35. 64
  36. 0.00068
  37. 0.0038
  38. 0.00012
  39. 729
  40. 9

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