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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 653 · 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 10⁻² (as a fraction)? =
  2. 2.Write 4 × 10⁻¹ as a decimal. =
  3. 3.Write 1,50,000 in standard form as 1.5 × 10ⁿ. What is n?
  4. 4.Write 2,20,00,000 in standard form as 2.2 × 10ⁿ. What is n?
  5. 5.Write 8.2 × 10⁻² as a decimal. =
  6. 6.Write 2⁵ × 2⁵ as a single power 2ⁿ. What is n?
  7. 7.What is the value of 3⁶ × 3⁻⁴? =
  8. 8.What is the value of 5⁵ × 5⁻²? =
  9. 9.What is the value of 10³? =
  10. 10.Write 2.9 × 10⁻² as a decimal. =
  11. 11.What is the value of 2¹²? =
  12. 12.What is the value of 3¹⁰? =
  13. 13.Write (3⁸)⁸ as a single power 3ⁿ. What is n?
  14. 14.What is the value of 2³? =
  15. 15.Write 9.3 × 10⁻² as a decimal. =
  16. 16.What is the value of (1/5)⁻²? =
  17. 17.1.2 × 10⁶ =
  18. 18.What is the value of 7⁻¹ (as a fraction)? =
  19. 19.Write 4.8 × 10⁻³ as a decimal. =
  20. 20.Write 1.7 × 10⁻³ as a decimal. =
  21. 21.Write 4⁸ ÷ 4⁵ as a single power 4ⁿ. What is n?
  22. 22.What is the value of 2¹ × 2⁻⁶? =
  23. 23.Write 9⁴ × 9² as a single power 9ⁿ. What is n?
  24. 24.What is the value of 2⁻⁶ (as a fraction)? =
  25. 25.Write 4⁶ × 4⁸ as a single power 4ⁿ. What is n?
  26. 26.8.2 × 10⁷ =
  27. 27.What is the value of 2¹⁴? =
  28. 28.Write 7.3 × 10⁻² as a decimal. =
  29. 29.What is the value of 6⁵? =
  30. 30.What is the value of 3⁻² (as a fraction)? =
  31. 31.Write 3,30,000 in standard form as 3.3 × 10ⁿ. What is n?
  32. 32.What is the value of 2⁻⁸ (as a fraction)? =
  33. 33.What is the value of (1/8)⁻¹? =
  34. 34.What is the value of (2/3)⁻²? =
  35. 35.9.5 × 10⁵ =
  36. 36.What is the value of 2³ × 2⁻⁵? =
  37. 37.7.6 × 10⁵ =
  38. 38.8.6 × 10⁴ =
  39. 39.Write 9.8 × 10⁻¹ as a decimal. =
  40. 40.Write (5⁷)⁸ as a single power 5ⁿ. What is n?

Answer key

  1. 1/100
  2. 0.4
  3. 5
  4. 7
  5. 0.082
  6. 10
  7. 9
  8. 125
  9. 1000
  10. 0.029
  11. 4096
  12. 59049
  13. 64
  14. 8
  15. 0.093
  16. 25
  17. 1200000
  18. 1/7
  19. 0.0048
  20. 0.0017
  21. 3
  22. 1/32
  23. 6
  24. 1/64
  25. 14
  26. 82000000
  27. 16384
  28. 0.073
  29. 7776
  30. 1/9
  31. 5
  32. 1/256
  33. 8
  34. 9/4
  35. 950000
  36. 1/4
  37. 760000
  38. 86000
  39. 0.98
  40. 56

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