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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 6 · 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 (1/3)⁻¹? =
  2. 2.What is the value of 2² × 2⁻⁶? =
  3. 3.What is the value of 2⁵? =
  4. 4.What is the value of 8⁵? =
  5. 5.What is the value of 3⁴ × 3⁻¹? =
  6. 6.Write 9.5 × 10⁻⁴ as a decimal. =
  7. 7.What is the value of 2⁻⁶ (as a fraction)? =
  8. 8.What is the value of 2³ × 2⁻²? =
  9. 9.What is the value of 2¹⁰? =
  10. 10.What is the value of 6⁴? =
  11. 11.Write 3.7 × 10⁻¹ as a decimal. =
  12. 12.What is the value of 5⁵? =
  13. 13.Write 63,00,000 in standard form as 6.3 × 10ⁿ. What is n?
  14. 14.What is the value of 5⁶? =
  15. 15.Write 37,00,000 in standard form as 3.7 × 10ⁿ. What is n?
  16. 16.Write 3.3 × 10⁻³ as a decimal. =
  17. 17.What is the value of 2² × 2⁻³? =
  18. 18.What is the value of 10⁻² (as a fraction)? =
  19. 19.Write (9⁷)⁷ as a single power 9ⁿ. What is n?
  20. 20.Write 5.3 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 2¹ × 2⁻⁶? =
  22. 22.Write 33,000 in standard form as 3.3 × 10ⁿ. What is n?
  23. 23.Write 5.4 × 10⁻³ as a decimal. =
  24. 24.Write 6.2 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 10⁴? =
  26. 26.What is the value of 3⁵? =
  27. 27.Write (7⁴)⁷ as a single power 7ⁿ. What is n?
  28. 28.Write (6⁴)² as a single power 6ⁿ. What is n?
  29. 29.What is the value of 3¹ × 3⁻⁴? =
  30. 30.What is the value of 10³? =
  31. 31.Write 1,300 in standard form as 1.3 × 10ⁿ. What is n?
  32. 32.Write 3.2 × 10⁻⁴ as a decimal. =
  33. 33.Write 3.3 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 5⁶ × 5⁻⁶? =
  35. 35.What is the value of 5³ × 5⁻⁶? =
  36. 36.Write 8⁴ × 8³ as a single power 8ⁿ. What is n?
  37. 37.What is the value of 2¹⁴? =
  38. 38.Write 3⁹ × 3⁶ as a single power 3ⁿ. What is n?
  39. 39.What is the value of 5⁴? =
  40. 40.Write 1.5 × 10⁻⁴ as a decimal. =

Answer key

  1. 3
  2. 1/16
  3. 32
  4. 32768
  5. 27
  6. 0.00095
  7. 1/64
  8. 2
  9. 1024
  10. 1296
  11. 0.37
  12. 3125
  13. 6
  14. 15625
  15. 6
  16. 0.0033
  17. 1/2
  18. 1/100
  19. 49
  20. 0.53
  21. 1/32
  22. 4
  23. 0.0054
  24. 0.62
  25. 10000
  26. 243
  27. 28
  28. 8
  29. 1/27
  30. 1000
  31. 3
  32. 0.00032
  33. 0.33
  34. 1
  35. 1/125
  36. 7
  37. 16384
  38. 15
  39. 625
  40. 0.00015

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