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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 348 · 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 5⁵ × 5⁻⁴? =
  2. 2.Write 7.6 × 10⁻² as a decimal. =
  3. 3.Write 5.6 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of (3/4)⁻¹? =
  5. 5.Write 1.3 × 10⁻² as a decimal. =
  6. 6.What is the value of (5/8)⁻¹? =
  7. 7.Write 5⁹ × 5² as a single power 5ⁿ. What is n?
  8. 8.What is the value of 3⁶? =
  9. 9.Write 3¹¹ ÷ 3⁹ as a single power 3ⁿ. What is n?
  10. 10.Write 4⁶ × 4³ as a single power 4ⁿ. What is n?
  11. 11.What is the value of 4⁴? =
  12. 12.What is the value of 2¹⁶? =
  13. 13.What is the value of (1/4)⁻¹? =
  14. 14.Write (7⁸)⁹ as a single power 7ⁿ. What is n?
  15. 15.What is the value of 4⁻¹ (as a fraction)? =
  16. 16.Write 4,700 in standard form as 4.7 × 10ⁿ. What is n?
  17. 17.Write 6⁴ × 6² as a single power 6ⁿ. What is n?
  18. 18.Write 3,10,000 in standard form as 3.1 × 10ⁿ. What is n?
  19. 19.3.7 × 10³ =
  20. 20.What is the value of 2¹⁴? =
  21. 21.What is the value of 3⁻⁵ (as a fraction)? =
  22. 22.What is the value of 2⁻⁴ (as a fraction)? =
  23. 23.What is the value of 2⁴ × 2⁻⁶? =
  24. 24.Write 9⁶ ÷ 9² as a single power 9ⁿ. What is n?
  25. 25.Write 5³ × 5⁸ as a single power 5ⁿ. What is n?
  26. 26.What is the value of 10³ × 10⁻³? =
  27. 27.What is the value of (5/7)⁻²? =
  28. 28.Write 2.2 × 10⁻³ as a decimal. =
  29. 29.What is the value of 5⁴ × 5⁻³? =
  30. 30.What is the value of 6³? =
  31. 31.What is the value of 2¹⁰? =
  32. 32.Write 45,000 in standard form as 4.5 × 10ⁿ. What is n?
  33. 33.What is the value of 2⁴ × 2⁻³? =
  34. 34.Write 170 in standard form as 1.7 × 10ⁿ. What is n?
  35. 35.What is the value of 10⁶ × 10⁻⁶? =
  36. 36.1.9 × 10² =
  37. 37.Write 4¹¹ ÷ 4³ as a single power 4ⁿ. What is n?
  38. 38.What is the value of 5² × 5⁻⁵? =
  39. 39.What is the value of 2¹¹? =
  40. 40.What is the value of 3⁻⁴ (as a fraction)? =

Answer key

  1. 5
  2. 0.076
  3. 0.00056
  4. 4/3
  5. 0.013
  6. 8/5
  7. 11
  8. 729
  9. 2
  10. 9
  11. 256
  12. 65536
  13. 4
  14. 72
  15. 1/4
  16. 3
  17. 6
  18. 5
  19. 3700
  20. 16384
  21. 1/243
  22. 1/16
  23. 1/4
  24. 4
  25. 11
  26. 1
  27. 49/25
  28. 0.0022
  29. 5
  30. 216
  31. 1024
  32. 4
  33. 2
  34. 2
  35. 1
  36. 190
  37. 8
  38. 1/125
  39. 2048
  40. 1/81

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