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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 823 · 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 660 in standard form as 6.6 × 10ⁿ. What is n?
  2. 2.Write 930 in standard form as 9.3 × 10ⁿ. What is n?
  3. 3.Write 5⁷ × 5⁸ as a single power 5ⁿ. What is n?
  4. 4.What is the value of (3/4)⁻²? =
  5. 5.What is the value of 3¹ × 3⁻²? =
  6. 6.Write (5⁵)⁴ as a single power 5ⁿ. What is n?
  7. 7.What is the value of 8³? =
  8. 8.What is the value of (1/3)⁻¹? =
  9. 9.What is the value of 2¹²? =
  10. 10.What is the value of 10³? =
  11. 11.What is the value of 2⁴? =
  12. 12.What is the value of 2² × 2⁻²? =
  13. 13.Write 5.4 × 10⁻⁴ as a decimal. =
  14. 14.What is the value of 10³ × 10⁻⁴? =
  15. 15.Write 6⁸ ÷ 6³ as a single power 6ⁿ. What is n?
  16. 16.Write 7³ × 7² as a single power 7ⁿ. What is n?
  17. 17.Write 2,30,00,000 in standard form as 2.3 × 10ⁿ. What is n?
  18. 18.What is the value of 3² × 3⁻⁶? =
  19. 19.6.6 × 10³ =
  20. 20.What is the value of 10⁻³ (as a fraction)? =
  21. 21.What is the value of 2² × 2⁻⁴? =
  22. 22.Write 3⁷ ÷ 3⁴ as a single power 3ⁿ. What is n?
  23. 23.What is the value of 10⁴ × 10⁻⁴? =
  24. 24.What is the value of 7²? =
  25. 25.Write 30,00,000 in standard form as 3 × 10ⁿ. What is n?
  26. 26.Write 75,000 in standard form as 7.5 × 10ⁿ. What is n?
  27. 27.What is the value of 2⁶ × 2⁻²? =
  28. 28.Write 37,000 in standard form as 3.7 × 10ⁿ. What is n?
  29. 29.What is the value of 3³? =
  30. 30.What is the value of 4⁸? =
  31. 31.Write 9,60,000 in standard form as 9.6 × 10ⁿ. What is n?
  32. 32.7.5 × 10³ =
  33. 33.What is the value of 3⁴ × 3⁻⁵? =
  34. 34.What is the value of 4³? =
  35. 35.What is the value of (3/4)⁻¹? =
  36. 36.What is the value of 2¹ × 2⁻²? =
  37. 37.4.2 × 10⁶ =
  38. 38.Write 3,70,000 in standard form as 3.7 × 10ⁿ. What is n?
  39. 39.What is the value of 3² × 3⁻³? =
  40. 40.What is the value of 2¹³? =

Answer key

  1. 2
  2. 2
  3. 15
  4. 16/9
  5. 1/3
  6. 20
  7. 512
  8. 3
  9. 4096
  10. 1000
  11. 16
  12. 1
  13. 0.00054
  14. 1/10
  15. 5
  16. 5
  17. 7
  18. 1/81
  19. 6600
  20. 1/1000
  21. 1/4
  22. 3
  23. 1
  24. 49
  25. 6
  26. 4
  27. 16
  28. 4
  29. 27
  30. 65536
  31. 5
  32. 7500
  33. 1/3
  34. 64
  35. 4/3
  36. 1/2
  37. 4200000
  38. 5
  39. 1/3
  40. 8192

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