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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 37 · 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 65,000 in standard form as 6.5 × 10ⁿ. What is n?
  2. 2.Write 6.9 × 10⁻³ as a decimal. =
  3. 3.What is the value of 5² × 5⁻⁵? =
  4. 4.Write 8,700 in standard form as 8.7 × 10ⁿ. What is n?
  5. 5.Write 6⁸ ÷ 6⁴ as a single power 6ⁿ. What is n?
  6. 6.Write 9,70,00,000 in standard form as 9.7 × 10ⁿ. What is n?
  7. 7.What is the value of 3⁵ × 3⁻¹? =
  8. 8.Write 2⁶ ÷ 2² as a single power 2ⁿ. What is n?
  9. 9.Write (5²)⁷ as a single power 5ⁿ. What is n?
  10. 10.What is the value of 10⁵ × 10⁻¹? =
  11. 11.Write 6⁴ × 6⁸ as a single power 6ⁿ. What is n?
  12. 12.Write 8⁷ × 8⁹ as a single power 8ⁿ. What is n?
  13. 13.Write 4 × 10⁻² as a decimal. =
  14. 14.Write (6⁹)⁸ as a single power 6ⁿ. What is n?
  15. 15.1.1 × 10⁵ =
  16. 16.What is the value of 4⁵? =
  17. 17.What is the value of (7/8)⁻²? =
  18. 18.Write (2⁷)⁵ as a single power 2ⁿ. What is n?
  19. 19.What is the value of 7⁵? =
  20. 20.Write 6 × 10⁻³ as a decimal. =
  21. 21.What is the value of 5⁶ × 5⁻⁶? =
  22. 22.Write 110 in standard form as 1.1 × 10ⁿ. What is n?
  23. 23.What is the value of 5⁷? =
  24. 24.Write 4,800 in standard form as 4.8 × 10ⁿ. What is n?
  25. 25.Write 6⁵ × 6³ as a single power 6ⁿ. What is n?
  26. 26.Write 7⁷ × 7⁸ as a single power 7ⁿ. What is n?
  27. 27.What is the value of 8⁴? =
  28. 28.What is the value of 2⁴ × 2⁻¹? =
  29. 29.Write 8,10,00,000 in standard form as 8.1 × 10ⁿ. What is n?
  30. 30.What is the value of 3⁶ × 3⁻⁵? =
  31. 31.What is the value of 3⁻² (as a fraction)? =
  32. 32.What is the value of 2¹²? =
  33. 33.Write 3⁵ × 3⁴ as a single power 3ⁿ. What is n?
  34. 34.Write 7 × 10⁻² as a decimal. =
  35. 35.Write 4⁷ × 4⁷ as a single power 4ⁿ. What is n?
  36. 36.What is the value of 3⁴ × 3⁻²? =
  37. 37.Write 2⁶ ÷ 2⁴ as a single power 2ⁿ. What is n?
  38. 38.Write 8⁹ × 8² as a single power 8ⁿ. What is n?
  39. 39.Write 1.4 × 10⁻² as a decimal. =
  40. 40.Write 8.9 × 10⁻³ as a decimal. =

Answer key

  1. 4
  2. 0.0069
  3. 1/125
  4. 3
  5. 4
  6. 7
  7. 81
  8. 4
  9. 14
  10. 10000
  11. 12
  12. 16
  13. 0.04
  14. 72
  15. 110000
  16. 1024
  17. 64/49
  18. 35
  19. 16807
  20. 0.006
  21. 1
  22. 2
  23. 78125
  24. 3
  25. 8
  26. 15
  27. 4096
  28. 8
  29. 7
  30. 3
  31. 1/9
  32. 4096
  33. 9
  34. 0.07
  35. 14
  36. 9
  37. 2
  38. 11
  39. 0.014
  40. 0.0089

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