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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 755 · 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 8³? =
  2. 2.Write 180 in standard form as 1.8 × 10ⁿ. What is n?
  3. 3.What is the value of 3⁷? =
  4. 4.What is the value of (2/9)⁻²? =
  5. 5.Write 8.4 × 10⁻³ as a decimal. =
  6. 6.What is the value of 9⁵? =
  7. 7.4.2 × 10⁷ =
  8. 8.Write 5.8 × 10⁻² as a decimal. =
  9. 9.What is the value of 10⁻³ (as a fraction)? =
  10. 10.What is the value of (3/5)⁻²? =
  11. 11.5.6 × 10⁵ =
  12. 12.What is the value of 10³ × 10⁻⁴? =
  13. 13.What is the value of 2⁵ × 2⁻²? =
  14. 14.Write 33,000 in standard form as 3.3 × 10ⁿ. What is n?
  15. 15.Write 1,200 in standard form as 1.2 × 10ⁿ. What is n?
  16. 16.What is the value of 3⁴ × 3⁻⁶? =
  17. 17.What is the value of 2² × 2⁻⁶? =
  18. 18.Write 9.3 × 10⁻³ as a decimal. =
  19. 19.Write 2.1 × 10⁻¹ as a decimal. =
  20. 20.Write (2⁹)³ as a single power 2ⁿ. What is n?
  21. 21.What is the value of 2¹³? =
  22. 22.Write 9,60,000 in standard form as 9.6 × 10ⁿ. What is n?
  23. 23.What is the value of 2³ × 2⁻⁴? =
  24. 24.What is the value of 2⁶ × 2⁻⁵? =
  25. 25.Write 1.6 × 10⁻⁴ as a decimal. =
  26. 26.Write (3⁴)² as a single power 3ⁿ. What is n?
  27. 27.What is the value of 3²? =
  28. 28.Write 5⁴ × 5⁶ as a single power 5ⁿ. What is n?
  29. 29.What is the value of 5³? =
  30. 30.Write 6.9 × 10⁻³ as a decimal. =
  31. 31.Write (3⁶)⁸ as a single power 3ⁿ. What is n?
  32. 32.Write (6⁶)⁸ as a single power 6ⁿ. What is n?
  33. 33.What is the value of 5³ × 5⁻¹? =
  34. 34.6.6 × 10⁷ =
  35. 35.Write 1.7 × 10⁻¹ as a decimal. =
  36. 36.Write 8.9 × 10⁻⁴ as a decimal. =
  37. 37.What is the value of 6²? =
  38. 38.What is the value of 2⁴ × 2⁻²? =
  39. 39.What is the value of 2⁻⁴ (as a fraction)? =
  40. 40.Write 6² × 6⁷ as a single power 6ⁿ. What is n?

Answer key

  1. 512
  2. 2
  3. 2187
  4. 81/4
  5. 0.0084
  6. 59049
  7. 42000000
  8. 0.058
  9. 1/1000
  10. 25/9
  11. 560000
  12. 1/10
  13. 8
  14. 4
  15. 3
  16. 1/9
  17. 1/16
  18. 0.0093
  19. 0.21
  20. 27
  21. 8192
  22. 5
  23. 1/2
  24. 2
  25. 0.00016
  26. 8
  27. 9
  28. 10
  29. 125
  30. 0.0069
  31. 48
  32. 48
  33. 25
  34. 66000000
  35. 0.17
  36. 0.00089
  37. 36
  38. 4
  39. 1/16
  40. 9

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