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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 212 · 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 10⁻³ (as a fraction)? =
  2. 2.Write 7⁹ × 7³ as a single power 7ⁿ. What is n?
  3. 3.Write 2³ × 2⁹ as a single power 2ⁿ. What is n?
  4. 4.What is the value of (2/3)⁻²? =
  5. 5.What is the value of 2⁶? =
  6. 6.What is the value of 4⁻¹ (as a fraction)? =
  7. 7.Write 9⁸ × 9⁹ as a single power 9ⁿ. What is n?
  8. 8.What is the value of 7⁻² (as a fraction)? =
  9. 9.Write (2⁴)³ as a single power 2ⁿ. What is n?
  10. 10.What is the value of 2⁴ × 2⁻⁶? =
  11. 11.Write 1,800 in standard form as 1.8 × 10ⁿ. What is n?
  12. 12.Write 4.3 × 10⁻² as a decimal. =
  13. 13.What is the value of 2¹ × 2⁻⁵? =
  14. 14.Write 3⁴ ÷ 3² as a single power 3ⁿ. What is n?
  15. 15.What is the value of 2² × 2⁻¹? =
  16. 16.What is the value of 5⁶ × 5⁻⁵? =
  17. 17.What is the value of 4⁷? =
  18. 18.Write 1.7 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 5⁻⁴ (as a fraction)? =
  20. 20.What is the value of 2³? =
  21. 21.What is the value of (5/8)⁻²? =
  22. 22.Write 7¹² ÷ 7⁴ as a single power 7ⁿ. What is n?
  23. 23.Write 2¹² ÷ 2⁹ as a single power 2ⁿ. What is n?
  24. 24.What is the value of 2⁹? =
  25. 25.8.3 × 10⁴ =
  26. 26.What is the value of 2⁸? =
  27. 27.Write 4,400 in standard form as 4.4 × 10ⁿ. What is n?
  28. 28.Write 8.4 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 10⁵ × 10⁻³? =
  30. 30.2.1 × 10² =
  31. 31.Write (5²)⁶ as a single power 5ⁿ. What is n?
  32. 32.What is the value of 5³? =
  33. 33.Write 5 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 2⁷? =
  35. 35.Write 4⁷ × 4⁵ as a single power 4ⁿ. What is n?
  36. 36.Write 3.8 × 10⁻⁴ as a decimal. =
  37. 37.What is the value of 2¹ × 2⁻³? =
  38. 38.Write 2¹¹ ÷ 2⁴ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 4⁵? =
  40. 40.What is the value of 10⁵? =

Answer key

  1. 1/1000
  2. 12
  3. 12
  4. 9/4
  5. 64
  6. 1/4
  7. 17
  8. 1/49
  9. 12
  10. 1/4
  11. 3
  12. 0.043
  13. 1/16
  14. 2
  15. 2
  16. 5
  17. 16384
  18. 0.00017
  19. 1/625
  20. 8
  21. 64/25
  22. 8
  23. 3
  24. 512
  25. 83000
  26. 256
  27. 3
  28. 0.84
  29. 100
  30. 210
  31. 12
  32. 125
  33. 0.5
  34. 128
  35. 12
  36. 0.00038
  37. 1/4
  38. 7
  39. 1024
  40. 100000

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