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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 692 · 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 10⁻³ (as a fraction)? =
  2. 2.What is the value of 3²? =
  3. 3.What is the value of 5⁵ × 5⁻⁶? =
  4. 4.Write 1.5 × 10⁻¹ as a decimal. =
  5. 5.What is the value of 8³? =
  6. 6.Write (7⁶)⁸ as a single power 7ⁿ. What is n?
  7. 7.What is the value of 2²? =
  8. 8.What is the value of (3/8)⁻²? =
  9. 9.What is the value of 3¹ × 3⁻³? =
  10. 10.What is the value of 10³ × 10⁻³? =
  11. 11.Write 2 × 10⁻⁴ as a decimal. =
  12. 12.What is the value of 5³ × 5⁻³? =
  13. 13.Write 3.7 × 10⁻³ as a decimal. =
  14. 14.Write 900 in standard form as 9 × 10ⁿ. What is n?
  15. 15.What is the value of 2² × 2⁻³? =
  16. 16.Write 460 in standard form as 4.6 × 10ⁿ. What is n?
  17. 17.What is the value of 3⁻⁶ (as a fraction)? =
  18. 18.Write 9¹⁰ ÷ 9⁷ as a single power 9ⁿ. What is n?
  19. 19.Write 3.1 × 10⁻¹ as a decimal. =
  20. 20.4.5 × 10⁴ =
  21. 21.Write 8.2 × 10⁻⁴ as a decimal. =
  22. 22.Write 4³ × 4⁴ as a single power 4ⁿ. What is n?
  23. 23.Write 1,200 in standard form as 1.2 × 10ⁿ. What is n?
  24. 24.What is the value of 5⁶ × 5⁻⁵? =
  25. 25.Write 4⁶ ÷ 4² as a single power 4ⁿ. What is n?
  26. 26.Write 1.1 × 10⁻³ as a decimal. =
  27. 27.Write 2,10,000 in standard form as 2.1 × 10ⁿ. What is n?
  28. 28.What is the value of 10²? =
  29. 29.What is the value of 8⁻¹ (as a fraction)? =
  30. 30.What is the value of (7/8)⁻²? =
  31. 31.What is the value of 3² × 3⁻²? =
  32. 32.Write 9⁹ ÷ 9² as a single power 9ⁿ. What is n?
  33. 33.9.4 × 10⁵ =
  34. 34.What is the value of 2¹²? =
  35. 35.What is the value of 9²? =
  36. 36.What is the value of (3/7)⁻¹? =
  37. 37.What is the value of 2⁻⁶ (as a fraction)? =
  38. 38.What is the value of (4/7)⁻¹? =
  39. 39.Write 1.5 × 10⁻² as a decimal. =
  40. 40.Write 810 in standard form as 8.1 × 10ⁿ. What is n?

Answer key

  1. 1/1000
  2. 9
  3. 1/5
  4. 0.15
  5. 512
  6. 48
  7. 4
  8. 64/9
  9. 1/9
  10. 1
  11. 0.0002
  12. 1
  13. 0.0037
  14. 2
  15. 1/2
  16. 2
  17. 1/729
  18. 3
  19. 0.31
  20. 45000
  21. 0.00082
  22. 7
  23. 3
  24. 5
  25. 4
  26. 0.0011
  27. 5
  28. 100
  29. 1/8
  30. 64/49
  31. 1
  32. 7
  33. 940000
  34. 4096
  35. 81
  36. 7/3
  37. 1/64
  38. 7/4
  39. 0.015
  40. 2

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