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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 328 · 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 2⁴ × 2⁻⁶? =
  2. 2.Write 6⁴ × 6² as a single power 6ⁿ. What is n?
  3. 3.What is the value of 7⁵? =
  4. 4.What is the value of 10⁴ × 10⁻⁶? =
  5. 5.Write 6.1 × 10⁻² as a decimal. =
  6. 6.What is the value of 8⁻¹ (as a fraction)? =
  7. 7.What is the value of 5³ × 5⁻⁶? =
  8. 8.What is the value of 5⁶ × 5⁻²? =
  9. 9.Write 660 in standard form as 6.6 × 10ⁿ. What is n?
  10. 10.What is the value of (2/5)⁻¹? =
  11. 11.What is the value of 2⁶? =
  12. 12.What is the value of 2⁷? =
  13. 13.8.7 × 10⁴ =
  14. 14.What is the value of 3⁻⁵ (as a fraction)? =
  15. 15.What is the value of (5/6)⁻²? =
  16. 16.Write 1,100 in standard form as 1.1 × 10ⁿ. What is n?
  17. 17.What is the value of 6⁻³ (as a fraction)? =
  18. 18.What is the value of 2¹¹? =
  19. 19.What is the value of (5/7)⁻²? =
  20. 20.Write 8⁷ × 8³ as a single power 8ⁿ. What is n?
  21. 21.8.5 × 10⁵ =
  22. 22.1.3 × 10⁴ =
  23. 23.Write 1.1 × 10⁻⁴ as a decimal. =
  24. 24.What is the value of (5/8)⁻²? =
  25. 25.Write 5.5 × 10⁻¹ as a decimal. =
  26. 26.Write 5¹² ÷ 5⁷ as a single power 5ⁿ. What is n?
  27. 27.What is the value of 3⁴ × 3⁻²? =
  28. 28.Write 3¹² ÷ 3⁶ as a single power 3ⁿ. What is n?
  29. 29.What is the value of 10⁴ × 10⁻¹? =
  30. 30.What is the value of 9⁴? =
  31. 31.What is the value of 3⁶ × 3⁻⁴? =
  32. 32.Write 12,00,000 in standard form as 1.2 × 10ⁿ. What is n?
  33. 33.What is the value of 4⁴? =
  34. 34.What is the value of 10² × 10⁻⁵? =
  35. 35.Write 30,000 in standard form as 3 × 10ⁿ. What is n?
  36. 36.Write 6⁴ × 6⁴ as a single power 6ⁿ. What is n?
  37. 37.Write 2⁹ ÷ 2² as a single power 2ⁿ. What is n?
  38. 38.What is the value of 2¹⁵? =
  39. 39.What is the value of 4⁶? =
  40. 40.Write 2³ × 2⁹ as a single power 2ⁿ. What is n?

Answer key

  1. 1/4
  2. 6
  3. 16807
  4. 1/100
  5. 0.061
  6. 1/8
  7. 1/125
  8. 625
  9. 2
  10. 5/2
  11. 64
  12. 128
  13. 87000
  14. 1/243
  15. 36/25
  16. 3
  17. 1/216
  18. 2048
  19. 49/25
  20. 10
  21. 850000
  22. 13000
  23. 0.00011
  24. 64/25
  25. 0.55
  26. 5
  27. 9
  28. 6
  29. 1000
  30. 6561
  31. 9
  32. 6
  33. 256
  34. 1/1000
  35. 4
  36. 8
  37. 7
  38. 32768
  39. 4096
  40. 12

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