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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 148 · 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 5¹ × 5⁻³? =
  2. 2.7.9 × 10⁵ =
  3. 3.Write 3.7 × 10⁻³ as a decimal. =
  4. 4.What is the value of 2⁸? =
  5. 5.Write 9⁶ × 9² as a single power 9ⁿ. What is n?
  6. 6.Write (8³)⁹ as a single power 8ⁿ. What is n?
  7. 7.What is the value of 4⁻² (as a fraction)? =
  8. 8.Write (2³)⁷ as a single power 2ⁿ. What is n?
  9. 9.What is the value of (3/5)⁻¹? =
  10. 10.Write 5.8 × 10⁻² as a decimal. =
  11. 11.Write (2⁵)⁵ as a single power 2ⁿ. What is n?
  12. 12.What is the value of 3⁴ × 3⁻⁴? =
  13. 13.What is the value of 3³ × 3⁻²? =
  14. 14.What is the value of 2¹³? =
  15. 15.Write 9² × 9⁴ as a single power 9ⁿ. What is n?
  16. 16.Write (8⁹)⁵ as a single power 8ⁿ. What is n?
  17. 17.Write 4¹⁵ ÷ 4⁶ as a single power 4ⁿ. What is n?
  18. 18.Write 4.5 × 10⁻¹ as a decimal. =
  19. 19.What is the value of 5¹ × 5⁻⁶? =
  20. 20.Write 44,00,000 in standard form as 4.4 × 10ⁿ. What is n?
  21. 21.Write 5⁷ ÷ 5⁵ as a single power 5ⁿ. What is n?
  22. 22.What is the value of (2/3)⁻²? =
  23. 23.Write 8⁵ × 8⁴ as a single power 8ⁿ. What is n?
  24. 24.What is the value of 6³? =
  25. 25.What is the value of 10⁵? =
  26. 26.Write 85,000 in standard form as 8.5 × 10ⁿ. What is n?
  27. 27.4.5 × 10⁴ =
  28. 28.What is the value of 7⁴? =
  29. 29.What is the value of (1/2)⁻¹? =
  30. 30.What is the value of 3⁻⁶ (as a fraction)? =
  31. 31.What is the value of 8⁻³ (as a fraction)? =
  32. 32.Write 500 in standard form as 5 × 10ⁿ. What is n?
  33. 33.What is the value of 10² × 10⁻¹? =
  34. 34.What is the value of 2⁶ × 2⁻¹? =
  35. 35.What is the value of (4/7)⁻¹? =
  36. 36.Write 38,000 in standard form as 3.8 × 10ⁿ. What is n?
  37. 37.Write 69,00,000 in standard form as 6.9 × 10ⁿ. What is n?
  38. 38.Write 8,000 in standard form as 8 × 10ⁿ. What is n?
  39. 39.Write 4.3 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of (1/2)⁻²? =

Answer key

  1. 1/25
  2. 790000
  3. 0.0037
  4. 256
  5. 8
  6. 27
  7. 1/16
  8. 21
  9. 5/3
  10. 0.058
  11. 25
  12. 1
  13. 3
  14. 8192
  15. 6
  16. 45
  17. 9
  18. 0.45
  19. 1/3125
  20. 6
  21. 2
  22. 9/4
  23. 9
  24. 216
  25. 100000
  26. 4
  27. 45000
  28. 2401
  29. 2
  30. 1/729
  31. 1/512
  32. 2
  33. 10
  34. 32
  35. 7/4
  36. 4
  37. 6
  38. 3
  39. 0.00043
  40. 4

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