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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 624 · 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 10³ × 10⁻⁴? =
  2. 2.What is the value of 2⁻⁸ (as a fraction)? =
  3. 3.What is the value of 3⁶? =
  4. 4.What is the value of 3⁴ × 3⁻⁶? =
  5. 5.What is the value of 5³? =
  6. 6.What is the value of 3⁵? =
  7. 7.Write 6.4 × 10⁻¹ as a decimal. =
  8. 8.Write 55,00,000 in standard form as 5.5 × 10ⁿ. What is n?
  9. 9.Write 2¹⁴ ÷ 2⁸ as a single power 2ⁿ. What is n?
  10. 10.What is the value of 4³? =
  11. 11.What is the value of 8²? =
  12. 12.Write 380 in standard form as 3.8 × 10ⁿ. What is n?
  13. 13.What is the value of 3¹ × 3⁻¹? =
  14. 14.Write 3² × 3⁸ as a single power 3ⁿ. What is n?
  15. 15.What is the value of 2¹⁵? =
  16. 16.What is the value of 2¹⁶? =
  17. 17.Write 7,000 in standard form as 7 × 10ⁿ. What is n?
  18. 18.What is the value of 2⁻⁷ (as a fraction)? =
  19. 19.Write (9⁵)⁵ as a single power 9ⁿ. What is n?
  20. 20.What is the value of 8⁵? =
  21. 21.Write 2.6 × 10⁻³ as a decimal. =
  22. 22.5.2 × 10⁵ =
  23. 23.Write 96,000 in standard form as 9.6 × 10ⁿ. What is n?
  24. 24.What is the value of 2⁴ × 2⁻¹? =
  25. 25.Write 5.2 × 10⁻¹ as a decimal. =
  26. 26.Write (3⁹)⁸ as a single power 3ⁿ. What is n?
  27. 27.What is the value of 2⁻³ (as a fraction)? =
  28. 28.Write 3 × 10⁻¹ as a decimal. =
  29. 29.5.9 × 10⁶ =
  30. 30.Write 48,00,000 in standard form as 4.8 × 10ⁿ. What is n?
  31. 31.Write 4,30,000 in standard form as 4.3 × 10ⁿ. What is n?
  32. 32.Write 8⁹ ÷ 8³ as a single power 8ⁿ. What is n?
  33. 33.What is the value of 5⁶ × 5⁻³? =
  34. 34.What is the value of 5⁻¹ (as a fraction)? =
  35. 35.What is the value of 2⁵? =
  36. 36.Write 5⁶ × 5² as a single power 5ⁿ. What is n?
  37. 37.What is the value of 3⁸? =
  38. 38.What is the value of (4/7)⁻²? =
  39. 39.Write 2.7 × 10⁻² as a decimal. =
  40. 40.Write (4⁸)⁹ as a single power 4ⁿ. What is n?

Answer key

  1. 1/10
  2. 1/256
  3. 729
  4. 1/9
  5. 125
  6. 243
  7. 0.64
  8. 6
  9. 6
  10. 64
  11. 64
  12. 2
  13. 1
  14. 10
  15. 32768
  16. 65536
  17. 3
  18. 1/128
  19. 25
  20. 32768
  21. 0.0026
  22. 520000
  23. 4
  24. 8
  25. 0.52
  26. 72
  27. 1/8
  28. 0.3
  29. 5900000
  30. 6
  31. 5
  32. 6
  33. 125
  34. 1/5
  35. 32
  36. 8
  37. 6561
  38. 49/16
  39. 0.027
  40. 72

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