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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 860 · 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 6⁸ × 6⁹ as a single power 6ⁿ. What is n?
  2. 2.What is the value of (1/3)⁻¹? =
  3. 3.What is the value of 3¹⁰? =
  4. 4.Write 4 × 10⁻² as a decimal. =
  5. 5.Write 200 in standard form as 2 × 10ⁿ. What is n?
  6. 6.Write 2.7 × 10⁻³ as a decimal. =
  7. 7.What is the value of 5³ × 5⁻¹? =
  8. 8.What is the value of 2⁷? =
  9. 9.What is the value of 2⁻¹ (as a fraction)? =
  10. 10.What is the value of 3²? =
  11. 11.Write 2.7 × 10⁻¹ as a decimal. =
  12. 12.What is the value of 3⁵ × 3⁻⁴? =
  13. 13.What is the value of 2³ × 2⁻¹? =
  14. 14.What is the value of 4⁻³ (as a fraction)? =
  15. 15.Write 2.2 × 10⁻³ as a decimal. =
  16. 16.Write 27,00,000 in standard form as 2.7 × 10ⁿ. What is n?
  17. 17.Write 9.8 × 10⁻¹ as a decimal. =
  18. 18.What is the value of 10¹ × 10⁻⁶? =
  19. 19.Write 1.7 × 10⁻³ as a decimal. =
  20. 20.Write (6⁴)² as a single power 6ⁿ. What is n?
  21. 21.Write 1.1 × 10⁻² as a decimal. =
  22. 22.What is the value of 2² × 2⁻²? =
  23. 23.3.5 × 10² =
  24. 24.Write 3,40,00,000 in standard form as 3.4 × 10ⁿ. What is n?
  25. 25.What is the value of (2/3)⁻²? =
  26. 26.What is the value of 2¹¹? =
  27. 27.What is the value of 4⁴? =
  28. 28.What is the value of 5²? =
  29. 29.What is the value of 5³? =
  30. 30.2.6 × 10⁵ =
  31. 31.Write 3⁷ ÷ 3⁵ as a single power 3ⁿ. What is n?
  32. 32.What is the value of 2¹³? =
  33. 33.Write 2¹⁷ ÷ 2⁹ as a single power 2ⁿ. What is n?
  34. 34.Write 2.4 × 10⁻¹ as a decimal. =
  35. 35.Write 4⁶ × 4² as a single power 4ⁿ. What is n?
  36. 36.What is the value of 5⁴? =
  37. 37.What is the value of 3⁻⁶ (as a fraction)? =
  38. 38.7.9 × 10³ =
  39. 39.Write 2,600 in standard form as 2.6 × 10ⁿ. What is n?
  40. 40.What is the value of (1/2)⁻¹? =

Answer key

  1. 17
  2. 3
  3. 59049
  4. 0.04
  5. 2
  6. 0.0027
  7. 25
  8. 128
  9. 1/2
  10. 9
  11. 0.27
  12. 3
  13. 4
  14. 1/64
  15. 0.0022
  16. 6
  17. 0.98
  18. 1/100000
  19. 0.0017
  20. 8
  21. 0.011
  22. 1
  23. 350
  24. 7
  25. 9/4
  26. 2048
  27. 256
  28. 25
  29. 125
  30. 260000
  31. 2
  32. 8192
  33. 8
  34. 0.24
  35. 8
  36. 625
  37. 1/729
  38. 7900
  39. 3
  40. 2

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