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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 465 · 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 3² × 3⁶ as a single power 3ⁿ. What is n?
  2. 2.What is the value of 6⁵? =
  3. 3.What is the value of 2² × 2⁻¹? =
  4. 4.2.3 × 10⁷ =
  5. 5.Write 2.2 × 10⁻³ as a decimal. =
  6. 6.What is the value of 10¹ × 10⁻⁶? =
  7. 7.Write 890 in standard form as 8.9 × 10ⁿ. What is n?
  8. 8.Write 87,000 in standard form as 8.7 × 10ⁿ. What is n?
  9. 9.What is the value of 10⁻² (as a fraction)? =
  10. 10.What is the value of 2² × 2⁻⁵? =
  11. 11.Write 3.6 × 10⁻¹ as a decimal. =
  12. 12.Write 1.5 × 10⁻² as a decimal. =
  13. 13.What is the value of 2⁴ × 2⁻²? =
  14. 14.What is the value of 5³ × 5⁻⁴? =
  15. 15.What is the value of 2⁴? =
  16. 16.What is the value of (5/6)⁻²? =
  17. 17.Write 5 × 10⁻³ as a decimal. =
  18. 18.Write (5⁷)³ as a single power 5ⁿ. What is n?
  19. 19.Write 800 in standard form as 8 × 10ⁿ. What is n?
  20. 20.Write 2¹² ÷ 2⁸ as a single power 2ⁿ. What is n?
  21. 21.What is the value of 10⁵? =
  22. 22.What is the value of 10⁴ × 10⁻³? =
  23. 23.4.5 × 10⁷ =
  24. 24.Write 7,90,00,000 in standard form as 7.9 × 10ⁿ. What is n?
  25. 25.What is the value of 5⁻² (as a fraction)? =
  26. 26.What is the value of 9²? =
  27. 27.Write 4¹³ ÷ 4⁹ as a single power 4ⁿ. What is n?
  28. 28.Write 1.1 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 9⁴? =
  30. 30.What is the value of 2¹⁶? =
  31. 31.What is the value of 2⁻³ (as a fraction)? =
  32. 32.What is the value of 3⁹? =
  33. 33.Write 2 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 2⁻⁶ (as a fraction)? =
  35. 35.Write 57,00,000 in standard form as 5.7 × 10ⁿ. What is n?
  36. 36.What is the value of 2⁶? =
  37. 37.Write 200 in standard form as 2 × 10ⁿ. What is n?
  38. 38.What is the value of 3² × 3⁻¹? =
  39. 39.Write 2.6 × 10⁻² as a decimal. =
  40. 40.What is the value of 2⁻⁸ (as a fraction)? =

Answer key

  1. 8
  2. 7776
  3. 2
  4. 23000000
  5. 0.0022
  6. 1/100000
  7. 2
  8. 4
  9. 1/100
  10. 1/8
  11. 0.36
  12. 0.015
  13. 4
  14. 1/5
  15. 16
  16. 36/25
  17. 0.005
  18. 21
  19. 2
  20. 4
  21. 100000
  22. 10
  23. 45000000
  24. 7
  25. 1/25
  26. 81
  27. 4
  28. 0.11
  29. 6561
  30. 65536
  31. 1/8
  32. 19683
  33. 0.2
  34. 1/64
  35. 6
  36. 64
  37. 2
  38. 3
  39. 0.026
  40. 1/256

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