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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 292 · 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 4⁻² (as a fraction)? =
  2. 2.What is the value of (2/7)⁻¹? =
  3. 3.What is the value of 10¹ × 10⁻⁶? =
  4. 4.Write 2⁵ × 2⁷ as a single power 2ⁿ. What is n?
  5. 5.Write 4⁹ × 4³ as a single power 4ⁿ. What is n?
  6. 6.What is the value of 2⁴ × 2⁻⁴? =
  7. 7.What is the value of 2³ × 2⁻⁵? =
  8. 8.Write 1,500 in standard form as 1.5 × 10ⁿ. What is n?
  9. 9.Write 1.1 × 10⁻⁴ as a decimal. =
  10. 10.3.2 × 10⁶ =
  11. 11.Write 6.1 × 10⁻³ as a decimal. =
  12. 12.What is the value of 8³? =
  13. 13.Write (9⁸)⁵ as a single power 9ⁿ. What is n?
  14. 14.Write (7⁶)⁷ as a single power 7ⁿ. What is n?
  15. 15.Write 340 in standard form as 3.4 × 10ⁿ. What is n?
  16. 16.What is the value of (2/7)⁻²? =
  17. 17.Write 330 in standard form as 3.3 × 10ⁿ. What is n?
  18. 18.What is the value of 5⁻³ (as a fraction)? =
  19. 19.What is the value of 2² × 2⁻⁴? =
  20. 20.Write 2¹⁷ ÷ 2⁸ as a single power 2ⁿ. What is n?
  21. 21.What is the value of 10³ × 10⁻³? =
  22. 22.What is the value of 5² × 5⁻¹? =
  23. 23.Write 6.8 × 10⁻² as a decimal. =
  24. 24.Write (5²)³ as a single power 5ⁿ. What is n?
  25. 25.What is the value of 2¹⁶? =
  26. 26.Write 5⁷ × 5⁵ as a single power 5ⁿ. What is n?
  27. 27.What is the value of 3⁻⁴ (as a fraction)? =
  28. 28.What is the value of 10⁻² (as a fraction)? =
  29. 29.Write 50,000 in standard form as 5 × 10ⁿ. What is n?
  30. 30.What is the value of (2/3)⁻¹? =
  31. 31.1.4 × 10⁶ =
  32. 32.Write 4² × 4⁷ as a single power 4ⁿ. What is n?
  33. 33.What is the value of 6³? =
  34. 34.9.2 × 10⁴ =
  35. 35.4.2 × 10⁶ =
  36. 36.What is the value of 3² × 3⁻⁶? =
  37. 37.What is the value of 10⁴? =
  38. 38.What is the value of 2² × 2⁻¹? =
  39. 39.4.5 × 10⁷ =
  40. 40.What is the value of 3⁵ × 3⁻³? =

Answer key

  1. 1/16
  2. 7/2
  3. 1/100000
  4. 12
  5. 12
  6. 1
  7. 1/4
  8. 3
  9. 0.00011
  10. 3200000
  11. 0.0061
  12. 512
  13. 40
  14. 42
  15. 2
  16. 49/4
  17. 2
  18. 1/125
  19. 1/4
  20. 9
  21. 1
  22. 5
  23. 0.068
  24. 6
  25. 65536
  26. 12
  27. 1/81
  28. 1/100
  29. 4
  30. 3/2
  31. 1400000
  32. 9
  33. 216
  34. 92000
  35. 4200000
  36. 1/81
  37. 10000
  38. 2
  39. 45000000
  40. 9

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