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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 493 · 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 20,000 in standard form as 2 × 10ⁿ. What is n?
  2. 2.What is the value of 6⁻³ (as a fraction)? =
  3. 3.What is the value of 3⁶ × 3⁻²? =
  4. 4.Write 4⁹ ÷ 4⁵ as a single power 4ⁿ. What is n?
  5. 5.Write 3.2 × 10⁻¹ as a decimal. =
  6. 6.What is the value of 6²? =
  7. 7.What is the value of 3⁴ × 3⁻⁶? =
  8. 8.Write (9⁶)⁵ as a single power 9ⁿ. What is n?
  9. 9.Write (9⁸)⁶ as a single power 9ⁿ. What is n?
  10. 10.What is the value of 8⁴? =
  11. 11.Write 6.3 × 10⁻² as a decimal. =
  12. 12.What is the value of 10⁴? =
  13. 13.Write (8⁸)⁵ as a single power 8ⁿ. What is n?
  14. 14.What is the value of 5⁵? =
  15. 15.What is the value of 3⁴? =
  16. 16.What is the value of 2⁶ × 2⁻²? =
  17. 17.What is the value of 2¹ × 2⁻²? =
  18. 18.What is the value of 2⁻⁶ (as a fraction)? =
  19. 19.What is the value of 4⁻⁴ (as a fraction)? =
  20. 20.What is the value of 2² × 2⁻³? =
  21. 21.What is the value of 2¹⁴? =
  22. 22.Write 24,000 in standard form as 2.4 × 10ⁿ. What is n?
  23. 23.What is the value of 10¹ × 10⁻⁶? =
  24. 24.What is the value of 2¹ × 2⁻³? =
  25. 25.Write (9⁶)² as a single power 9ⁿ. What is n?
  26. 26.Write 7⁸ × 7³ as a single power 7ⁿ. What is n?
  27. 27.What is the value of (6/7)⁻¹? =
  28. 28.What is the value of 2⁶? =
  29. 29.What is the value of 10⁴ × 10⁻⁶? =
  30. 30.What is the value of (7/8)⁻²? =
  31. 31.Write 5.9 × 10⁻¹ as a decimal. =
  32. 32.3.5 × 10⁵ =
  33. 33.Write 4.5 × 10⁻¹ as a decimal. =
  34. 34.Write 8³ × 8³ as a single power 8ⁿ. What is n?
  35. 35.What is the value of 5⁶ × 5⁻¹? =
  36. 36.What is the value of 2⁵ × 2⁻¹? =
  37. 37.What is the value of 10³ × 10⁻²? =
  38. 38.Write 1.6 × 10⁻³ as a decimal. =
  39. 39.1.5 × 10⁴ =
  40. 40.Write 2.6 × 10⁻⁴ as a decimal. =

Answer key

  1. 4
  2. 1/216
  3. 81
  4. 4
  5. 0.32
  6. 36
  7. 1/9
  8. 30
  9. 48
  10. 4096
  11. 0.063
  12. 10000
  13. 40
  14. 3125
  15. 81
  16. 16
  17. 1/2
  18. 1/64
  19. 1/256
  20. 1/2
  21. 16384
  22. 4
  23. 1/100000
  24. 1/4
  25. 12
  26. 11
  27. 7/6
  28. 64
  29. 1/100
  30. 64/49
  31. 0.59
  32. 350000
  33. 0.45
  34. 6
  35. 3125
  36. 16
  37. 10
  38. 0.0016
  39. 15000
  40. 0.00026

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