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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 639 · 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 3⁵ × 3⁻¹? =
  2. 2.What is the value of 4⁻⁴ (as a fraction)? =
  3. 3.What is the value of 5³ × 5⁻⁵? =
  4. 4.What is the value of 5⁶ × 5⁻²? =
  5. 5.What is the value of 2⁵ × 2⁻¹? =
  6. 6.What is the value of 4⁵? =
  7. 7.What is the value of 5⁵? =
  8. 8.Write (3⁸)⁸ as a single power 3ⁿ. What is n?
  9. 9.Write 6.8 × 10⁻¹ as a decimal. =
  10. 10.Write 3.1 × 10⁻³ as a decimal. =
  11. 11.Write (5⁵)⁸ as a single power 5ⁿ. What is n?
  12. 12.Write (7⁵)⁹ as a single power 7ⁿ. What is n?
  13. 13.Write 9.6 × 10⁻³ as a decimal. =
  14. 14.What is the value of 2⁵ × 2⁻³? =
  15. 15.What is the value of 5¹ × 5⁻⁴? =
  16. 16.What is the value of 2⁵ × 2⁻⁴? =
  17. 17.What is the value of (3/7)⁻²? =
  18. 18.8.4 × 10⁵ =
  19. 19.5.6 × 10⁶ =
  20. 20.What is the value of 3⁴? =
  21. 21.What is the value of 3¹ × 3⁻²? =
  22. 22.Write 6¹⁴ ÷ 6⁶ as a single power 6ⁿ. What is n?
  23. 23.What is the value of 2²? =
  24. 24.What is the value of (8/9)⁻²? =
  25. 25.Write 6⁶ ÷ 6⁴ as a single power 6ⁿ. What is n?
  26. 26.What is the value of 5⁴ × 5⁻³? =
  27. 27.What is the value of 10⁻¹ (as a fraction)? =
  28. 28.What is the value of (1/3)⁻²? =
  29. 29.What is the value of 7²? =
  30. 30.What is the value of 3⁶ × 3⁻¹? =
  31. 31.What is the value of (5/8)⁻²? =
  32. 32.Write 9.9 × 10⁻¹ as a decimal. =
  33. 33.What is the value of 6⁴? =
  34. 34.Write 1.7 × 10⁻³ as a decimal. =
  35. 35.What is the value of 5²? =
  36. 36.8.1 × 10⁷ =
  37. 37.Write 21,00,000 in standard form as 2.1 × 10ⁿ. What is n?
  38. 38.What is the value of 5⁵ × 5⁻²? =
  39. 39.Write (2⁶)⁶ as a single power 2ⁿ. What is n?
  40. 40.What is the value of 2¹²? =

Answer key

  1. 81
  2. 1/256
  3. 1/25
  4. 625
  5. 16
  6. 1024
  7. 3125
  8. 64
  9. 0.68
  10. 0.0031
  11. 40
  12. 45
  13. 0.0096
  14. 4
  15. 1/125
  16. 2
  17. 49/9
  18. 840000
  19. 5600000
  20. 81
  21. 1/3
  22. 8
  23. 4
  24. 81/64
  25. 2
  26. 5
  27. 1/10
  28. 9
  29. 49
  30. 243
  31. 64/25
  32. 0.99
  33. 1296
  34. 0.0017
  35. 25
  36. 81000000
  37. 6
  38. 125
  39. 36
  40. 4096

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