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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 646 · 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.What is the value of (5/9)⁻²? =
  2. 2.Write (3⁵)⁷ as a single power 3ⁿ. What is n?
  3. 3.What is the value of 10⁵ × 10⁻⁶? =
  4. 4.Write 5.8 × 10⁻⁴ as a decimal. =
  5. 5.What is the value of 10¹ × 10⁻⁶? =
  6. 6.3.6 × 10⁵ =
  7. 7.What is the value of 2⁻⁴ (as a fraction)? =
  8. 8.Write 8.2 × 10⁻¹ as a decimal. =
  9. 9.Write (8³)² as a single power 8ⁿ. What is n?
  10. 10.Write (9⁶)⁷ as a single power 9ⁿ. What is n?
  11. 11.Write 760 in standard form as 7.6 × 10ⁿ. What is n?
  12. 12.What is the value of 2⁴ × 2⁻³? =
  13. 13.What is the value of 5³ × 5⁻²? =
  14. 14.What is the value of 5² × 5⁻²? =
  15. 15.What is the value of 2¹ × 2⁻⁴? =
  16. 16.What is the value of 4⁻³ (as a fraction)? =
  17. 17.Write 2.3 × 10⁻³ as a decimal. =
  18. 18.Write 5⁸ × 5⁶ as a single power 5ⁿ. What is n?
  19. 19.9 × 10⁴ =
  20. 20.What is the value of 2⁶? =
  21. 21.What is the value of 9⁴? =
  22. 22.Write (2⁸)⁶ as a single power 2ⁿ. What is n?
  23. 23.Write 8.3 × 10⁻¹ as a decimal. =
  24. 24.What is the value of 2³ × 2⁻¹? =
  25. 25.What is the value of 2⁻² (as a fraction)? =
  26. 26.1.1 × 10² =
  27. 27.What is the value of (1/2)⁻¹? =
  28. 28.Write 1.9 × 10⁻¹ as a decimal. =
  29. 29.Write 99,00,000 in standard form as 9.9 × 10ⁿ. What is n?
  30. 30.Write 660 in standard form as 6.6 × 10ⁿ. What is n?
  31. 31.What is the value of 3⁴? =
  32. 32.What is the value of (1/5)⁻¹? =
  33. 33.Write 5⁸ × 5⁴ as a single power 5ⁿ. What is n?
  34. 34.Write 2³ × 2⁴ as a single power 2ⁿ. What is n?
  35. 35.What is the value of 2¹⁴? =
  36. 36.What is the value of 3³? =
  37. 37.Write 260 in standard form as 2.6 × 10ⁿ. What is n?
  38. 38.Write (2²)⁹ as a single power 2ⁿ. What is n?
  39. 39.Write 4⁴ × 4⁷ as a single power 4ⁿ. What is n?
  40. 40.Write 4.8 × 10⁻¹ as a decimal. =

Answer key

  1. 81/25
  2. 35
  3. 1/10
  4. 0.00058
  5. 1/100000
  6. 360000
  7. 1/16
  8. 0.82
  9. 6
  10. 42
  11. 2
  12. 2
  13. 5
  14. 1
  15. 1/8
  16. 1/64
  17. 0.0023
  18. 14
  19. 90000
  20. 64
  21. 6561
  22. 48
  23. 0.83
  24. 4
  25. 1/4
  26. 110
  27. 2
  28. 0.19
  29. 6
  30. 2
  31. 81
  32. 5
  33. 12
  34. 7
  35. 16384
  36. 27
  37. 2
  38. 18
  39. 11
  40. 0.48

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