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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 335 · 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.Write 6,000 in standard form as 6 × 10ⁿ. What is n?
  2. 2.What is the value of 3¹⁰? =
  3. 3.Write 2⁶ ÷ 2² as a single power 2ⁿ. What is n?
  4. 4.What is the value of 2² × 2⁻³? =
  5. 5.What is the value of 2²? =
  6. 6.Write (7⁹)⁷ as a single power 7ⁿ. What is n?
  7. 7.What is the value of 5⁵ × 5⁻⁶? =
  8. 8.What is the value of 5³? =
  9. 9.What is the value of 4⁻¹ (as a fraction)? =
  10. 10.What is the value of 2⁻⁶ (as a fraction)? =
  11. 11.What is the value of 5³ × 5⁻²? =
  12. 12.What is the value of 2⁶? =
  13. 13.What is the value of (1/2)⁻²? =
  14. 14.What is the value of 2⁸? =
  15. 15.What is the value of 10³ × 10⁻⁵? =
  16. 16.Write 4,10,000 in standard form as 4.1 × 10ⁿ. What is n?
  17. 17.What is the value of 6⁻² (as a fraction)? =
  18. 18.Write 2.3 × 10⁻³ as a decimal. =
  19. 19.Write 2.2 × 10⁻¹ as a decimal. =
  20. 20.Write 3⁷ ÷ 3⁵ as a single power 3ⁿ. What is n?
  21. 21.What is the value of 4⁶? =
  22. 22.Write 6.7 × 10⁻⁴ as a decimal. =
  23. 23.What is the value of 2⁴ × 2⁻²? =
  24. 24.What is the value of 9³? =
  25. 25.What is the value of 3⁴ × 3⁻²? =
  26. 26.What is the value of 2³ × 2⁻¹? =
  27. 27.What is the value of 2⁷? =
  28. 28.Write 1.6 × 10⁻² as a decimal. =
  29. 29.What is the value of 2¹³? =
  30. 30.Write 2.1 × 10⁻² as a decimal. =
  31. 31.What is the value of 2³ × 2⁻³? =
  32. 32.What is the value of 5⁶? =
  33. 33.What is the value of 10⁵? =
  34. 34.What is the value of 6⁻¹ (as a fraction)? =
  35. 35.Write (3³)⁹ as a single power 3ⁿ. What is n?
  36. 36.Write 7¹⁷ ÷ 7⁹ as a single power 7ⁿ. What is n?
  37. 37.What is the value of 3⁻¹ (as a fraction)? =
  38. 38.Write 3.5 × 10⁻⁴ as a decimal. =
  39. 39.Write 4⁴ × 4² as a single power 4ⁿ. What is n?
  40. 40.What is the value of 3² × 3⁻⁴? =

Answer key

  1. 3
  2. 59049
  3. 4
  4. 1/2
  5. 4
  6. 63
  7. 1/5
  8. 125
  9. 1/4
  10. 1/64
  11. 5
  12. 64
  13. 4
  14. 256
  15. 1/100
  16. 5
  17. 1/36
  18. 0.0023
  19. 0.22
  20. 2
  21. 4096
  22. 0.00067
  23. 4
  24. 729
  25. 9
  26. 4
  27. 128
  28. 0.016
  29. 8192
  30. 0.021
  31. 1
  32. 15625
  33. 100000
  34. 1/6
  35. 27
  36. 8
  37. 1/3
  38. 0.00035
  39. 6
  40. 1/9

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