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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 332 · 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 3⁷ × 3⁸ as a single power 3ⁿ. What is n?
  2. 2.What is the value of 2⁵ × 2⁻¹? =
  3. 3.7 × 10³ =
  4. 4.Write (7⁸)⁷ as a single power 7ⁿ. What is n?
  5. 5.3.2 × 10⁴ =
  6. 6.Write 4¹⁵ ÷ 4⁹ as a single power 4ⁿ. What is n?
  7. 7.Write (9⁵)⁴ as a single power 9ⁿ. What is n?
  8. 8.Write 9.7 × 10⁻¹ as a decimal. =
  9. 9.Write (8²)³ as a single power 8ⁿ. What is n?
  10. 10.Write 1.3 × 10⁻¹ as a decimal. =
  11. 11.What is the value of 2⁻⁷ (as a fraction)? =
  12. 12.3.4 × 10⁷ =
  13. 13.6.2 × 10⁷ =
  14. 14.What is the value of (1/8)⁻²? =
  15. 15.What is the value of 7⁻¹ (as a fraction)? =
  16. 16.What is the value of 10⁵ × 10⁻¹? =
  17. 17.Write 5,800 in standard form as 5.8 × 10ⁿ. What is n?
  18. 18.Write 6.2 × 10⁻² as a decimal. =
  19. 19.What is the value of 2¹⁵? =
  20. 20.What is the value of 4⁻³ (as a fraction)? =
  21. 21.What is the value of 10⁶ × 10⁻²? =
  22. 22.What is the value of 10⁴? =
  23. 23.9.8 × 10³ =
  24. 24.Write 9⁸ × 9⁷ as a single power 9ⁿ. What is n?
  25. 25.What is the value of 2⁶ × 2⁻¹? =
  26. 26.Write 3⁹ × 3⁸ as a single power 3ⁿ. What is n?
  27. 27.What is the value of 3²? =
  28. 28.2.1 × 10⁴ =
  29. 29.Write 1.4 × 10⁻³ as a decimal. =
  30. 30.Write 4,50,000 in standard form as 4.5 × 10ⁿ. What is n?
  31. 31.Write (6⁵)⁶ as a single power 6ⁿ. What is n?
  32. 32.What is the value of (4/9)⁻¹? =
  33. 33.Write 3⁵ × 3² as a single power 3ⁿ. What is n?
  34. 34.What is the value of 4⁵? =
  35. 35.Write 6⁶ × 6⁸ as a single power 6ⁿ. What is n?
  36. 36.Write 6.7 × 10⁻¹ as a decimal. =
  37. 37.Write 31,000 in standard form as 3.1 × 10ⁿ. What is n?
  38. 38.Write (2⁵)³ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 2⁵ × 2⁻³? =
  40. 40.What is the value of 3¹ × 3⁻²? =

Answer key

  1. 15
  2. 16
  3. 7000
  4. 56
  5. 32000
  6. 6
  7. 20
  8. 0.97
  9. 6
  10. 0.13
  11. 1/128
  12. 34000000
  13. 62000000
  14. 64
  15. 1/7
  16. 10000
  17. 3
  18. 0.062
  19. 32768
  20. 1/64
  21. 10000
  22. 10000
  23. 9800
  24. 15
  25. 32
  26. 17
  27. 9
  28. 21000
  29. 0.0014
  30. 5
  31. 30
  32. 9/4
  33. 7
  34. 1024
  35. 14
  36. 0.67
  37. 4
  38. 15
  39. 4
  40. 1/3

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