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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 41 · 40 sums
TalentJR

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 2⁻³ (as a fraction)? =
  2. 2.2.1 × 10⁷ =
  3. 3.What is the value of 2¹ × 2⁻¹? =
  4. 4.Write 7⁴ × 7⁶ as a single power 7ⁿ. What is n?
  5. 5.What is the value of 3⁹? =
  6. 6.What is the value of 2⁻⁶ (as a fraction)? =
  7. 7.Write (8⁸)⁶ as a single power 8ⁿ. What is n?
  8. 8.Write 1,500 in standard form as 1.5 × 10ⁿ. What is n?
  9. 9.Write 5.5 × 10⁻¹ as a decimal. =
  10. 10.What is the value of 5⁶ × 5⁻⁵? =
  11. 11.Write 9² × 9⁴ as a single power 9ⁿ. What is n?
  12. 12.Write 6.9 × 10⁻¹ as a decimal. =
  13. 13.What is the value of (4/5)⁻¹? =
  14. 14.Write 5⁷ × 5⁶ as a single power 5ⁿ. What is n?
  15. 15.Write 7 × 10⁻² as a decimal. =
  16. 16.Write 6 × 10⁻⁴ as a decimal. =
  17. 17.What is the value of 2¹⁰? =
  18. 18.What is the value of 6²? =
  19. 19.What is the value of 5³? =
  20. 20.What is the value of 5³ × 5⁻²? =
  21. 21.What is the value of 7⁴? =
  22. 22.What is the value of (5/6)⁻²? =
  23. 23.6 × 10³ =
  24. 24.What is the value of 6⁴? =
  25. 25.Write 93,000 in standard form as 9.3 × 10ⁿ. What is n?
  26. 26.Write 8⁸ × 8⁹ as a single power 8ⁿ. What is n?
  27. 27.What is the value of 2⁶ × 2⁻³? =
  28. 28.Write (2⁴)⁶ as a single power 2ⁿ. What is n?
  29. 29.Write 6.1 × 10⁻⁴ as a decimal. =
  30. 30.What is the value of 5² × 5⁻³? =
  31. 31.What is the value of 3³ × 3⁻⁴? =
  32. 32.What is the value of 2⁴? =
  33. 33.What is the value of 8³? =
  34. 34.What is the value of 10² × 10⁻³? =
  35. 35.What is the value of 4⁻¹ (as a fraction)? =
  36. 36.Write 9 × 10⁻⁴ as a decimal. =
  37. 37.Write 6,400 in standard form as 6.4 × 10ⁿ. What is n?
  38. 38.Write (7³)⁷ as a single power 7ⁿ. What is n?
  39. 39.What is the value of (2/3)⁻¹? =
  40. 40.What is the value of 4⁴? =

Answer key

  1. 1/8
  2. 21000000
  3. 1
  4. 10
  5. 19683
  6. 1/64
  7. 48
  8. 3
  9. 0.55
  10. 5
  11. 6
  12. 0.69
  13. 5/4
  14. 13
  15. 0.07
  16. 0.0006
  17. 1024
  18. 36
  19. 125
  20. 5
  21. 2401
  22. 36/25
  23. 6000
  24. 1296
  25. 4
  26. 17
  27. 8
  28. 24
  29. 0.00061
  30. 1/5
  31. 1/3
  32. 16
  33. 512
  34. 1/10
  35. 1/4
  36. 0.0009
  37. 3
  38. 21
  39. 3/2
  40. 256

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