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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 206 · 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 9⁷ ÷ 9² as a single power 9ⁿ. What is n?
  2. 2.Write 550 in standard form as 5.5 × 10ⁿ. What is n?
  3. 3.What is the value of (3/4)⁻¹? =
  4. 4.3.9 × 10³ =
  5. 5.What is the value of 3¹ × 3⁻³? =
  6. 6.What is the value of 2⁷? =
  7. 7.Write 5.7 × 10⁻¹ as a decimal. =
  8. 8.9.9 × 10³ =
  9. 9.What is the value of 3⁴ × 3⁻⁴? =
  10. 10.What is the value of 10³ × 10⁻⁴? =
  11. 11.What is the value of 5⁻² (as a fraction)? =
  12. 12.Write (5²)⁶ as a single power 5ⁿ. What is n?
  13. 13.1.9 × 10⁶ =
  14. 14.What is the value of (2/5)⁻²? =
  15. 15.What is the value of 4⁻³ (as a fraction)? =
  16. 16.Write 7⁵ × 7⁶ as a single power 7ⁿ. What is n?
  17. 17.Write 4.9 × 10⁻² as a decimal. =
  18. 18.What is the value of 10⁵ × 10⁻³? =
  19. 19.4.5 × 10⁵ =
  20. 20.Write 2.7 × 10⁻² as a decimal. =
  21. 21.Write 4.1 × 10⁻² as a decimal. =
  22. 22.What is the value of 3² × 3⁻²? =
  23. 23.Write 9.5 × 10⁻² as a decimal. =
  24. 24.What is the value of 7³? =
  25. 25.Write 580 in standard form as 5.8 × 10ⁿ. What is n?
  26. 26.Write 1.7 × 10⁻² as a decimal. =
  27. 27.Write 1.4 × 10⁻³ as a decimal. =
  28. 28.Write 8.6 × 10⁻³ as a decimal. =
  29. 29.8.7 × 10⁵ =
  30. 30.Write 3.8 × 10⁻³ as a decimal. =
  31. 31.What is the value of 10⁴ × 10⁻³? =
  32. 32.What is the value of 2⁻⁸ (as a fraction)? =
  33. 33.What is the value of (1/2)⁻¹? =
  34. 34.What is the value of 3² × 3⁻³? =
  35. 35.Write 3 × 10⁻² as a decimal. =
  36. 36.Write 6¹⁵ ÷ 6⁷ as a single power 6ⁿ. What is n?
  37. 37.What is the value of 5²? =
  38. 38.Write 2⁸ × 2⁵ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 2³? =
  40. 40.Write 2.6 × 10⁻⁴ as a decimal. =

Answer key

  1. 5
  2. 2
  3. 4/3
  4. 3900
  5. 1/9
  6. 128
  7. 0.57
  8. 9900
  9. 1
  10. 1/10
  11. 1/25
  12. 12
  13. 1900000
  14. 25/4
  15. 1/64
  16. 11
  17. 0.049
  18. 100
  19. 450000
  20. 0.027
  21. 0.041
  22. 1
  23. 0.095
  24. 343
  25. 2
  26. 0.017
  27. 0.0014
  28. 0.0086
  29. 870000
  30. 0.0038
  31. 10
  32. 1/256
  33. 2
  34. 1/3
  35. 0.03
  36. 8
  37. 25
  38. 13
  39. 8
  40. 0.00026

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