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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 109 · 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 2¹² ÷ 2³ as a single power 2ⁿ. What is n?
  2. 2.Write 2⁷ × 2⁶ as a single power 2ⁿ. What is n?
  3. 3.What is the value of 4⁴? =
  4. 4.What is the value of 10⁻¹ (as a fraction)? =
  5. 5.Write 6.7 × 10⁻² as a decimal. =
  6. 6.Write 2.4 × 10⁻¹ as a decimal. =
  7. 7.5.3 × 10⁷ =
  8. 8.Write 4⁶ ÷ 4⁴ as a single power 4ⁿ. What is n?
  9. 9.Write 1,100 in standard form as 1.1 × 10ⁿ. What is n?
  10. 10.7.1 × 10² =
  11. 11.Write 9⁵ × 9⁸ as a single power 9ⁿ. What is n?
  12. 12.6.9 × 10⁴ =
  13. 13.What is the value of 9²? =
  14. 14.What is the value of 5¹ × 5⁻⁵? =
  15. 15.Write 7⁵ × 7² as a single power 7ⁿ. What is n?
  16. 16.Write 7³ × 7⁸ as a single power 7ⁿ. What is n?
  17. 17.What is the value of 10⁶ × 10⁻³? =
  18. 18.Write 64,00,000 in standard form as 6.4 × 10ⁿ. What is n?
  19. 19.What is the value of 3⁻¹ (as a fraction)? =
  20. 20.Write 3.5 × 10⁻⁴ as a decimal. =
  21. 21.Write 4 × 10⁻² as a decimal. =
  22. 22.Write 6² × 6⁴ as a single power 6ⁿ. What is n?
  23. 23.Write 25,000 in standard form as 2.5 × 10ⁿ. What is n?
  24. 24.Write 1.8 × 10⁻³ as a decimal. =
  25. 25.What is the value of 5⁵? =
  26. 26.Write 5,700 in standard form as 5.7 × 10ⁿ. What is n?
  27. 27.Write 7¹² ÷ 7⁵ as a single power 7ⁿ. What is n?
  28. 28.Write (6³)⁴ as a single power 6ⁿ. What is n?
  29. 29.Write 6⁵ × 6⁸ as a single power 6ⁿ. What is n?
  30. 30.Write 2⁷ × 2² as a single power 2ⁿ. What is n?
  31. 31.Write 3.1 × 10⁻⁴ as a decimal. =
  32. 32.What is the value of 5³ × 5⁻⁵? =
  33. 33.Write 2.6 × 10⁻⁴ as a decimal. =
  34. 34.Write (4⁶)⁹ as a single power 4ⁿ. What is n?
  35. 35.What is the value of 10¹ × 10⁻³? =
  36. 36.What is the value of 2⁶ × 2⁻⁵? =
  37. 37.What is the value of 2⁵ × 2⁻⁶? =
  38. 38.What is the value of 3⁵ × 3⁻⁵? =
  39. 39.What is the value of 2¹ × 2⁻²? =
  40. 40.Write (6⁸)⁴ as a single power 6ⁿ. What is n?

Answer key

  1. 9
  2. 13
  3. 256
  4. 1/10
  5. 0.067
  6. 0.24
  7. 53000000
  8. 2
  9. 3
  10. 710
  11. 13
  12. 69000
  13. 81
  14. 1/625
  15. 7
  16. 11
  17. 1000
  18. 6
  19. 1/3
  20. 0.00035
  21. 0.04
  22. 6
  23. 4
  24. 0.0018
  25. 3125
  26. 3
  27. 7
  28. 12
  29. 13
  30. 9
  31. 0.00031
  32. 1/25
  33. 0.00026
  34. 54
  35. 1/100
  36. 2
  37. 1/2
  38. 1
  39. 1/2
  40. 32

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