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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 275 · 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 5² × 5³ as a single power 5ⁿ. What is n?
  2. 2.6.6 × 10³ =
  3. 3.Write 3.2 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of 10¹ × 10⁻³? =
  5. 5.What is the value of 2⁴ × 2⁻⁵? =
  6. 6.Write 2.8 × 10⁻² as a decimal. =
  7. 7.Write 9.8 × 10⁻³ as a decimal. =
  8. 8.What is the value of 2³ × 2⁻⁴? =
  9. 9.What is the value of 9⁻³ (as a fraction)? =
  10. 10.What is the value of (7/8)⁻²? =
  11. 11.Write (2⁸)⁹ as a single power 2ⁿ. What is n?
  12. 12.What is the value of 8³? =
  13. 13.Write 8⁹ × 8⁸ as a single power 8ⁿ. What is n?
  14. 14.Write 5.7 × 10⁻³ as a decimal. =
  15. 15.What is the value of 3²? =
  16. 16.Write 7.8 × 10⁻² as a decimal. =
  17. 17.What is the value of (1/2)⁻²? =
  18. 18.Write (9⁸)⁸ as a single power 9ⁿ. What is n?
  19. 19.What is the value of 2⁻¹ (as a fraction)? =
  20. 20.Write 5⁷ × 5⁶ as a single power 5ⁿ. What is n?
  21. 21.Write 540 in standard form as 5.4 × 10ⁿ. What is n?
  22. 22.Write 4⁶ × 4⁵ as a single power 4ⁿ. What is n?
  23. 23.What is the value of (5/8)⁻¹? =
  24. 24.What is the value of 2⁵ × 2⁻⁵? =
  25. 25.What is the value of (2/7)⁻¹? =
  26. 26.What is the value of (3/8)⁻¹? =
  27. 27.What is the value of 4³? =
  28. 28.Write 3.1 × 10⁻¹ as a decimal. =
  29. 29.Write 1,60,00,000 in standard form as 1.6 × 10ⁿ. What is n?
  30. 30.What is the value of 6⁴? =
  31. 31.Write 1,800 in standard form as 1.8 × 10ⁿ. What is n?
  32. 32.What is the value of 5⁶ × 5⁻¹? =
  33. 33.What is the value of 3¹ × 3⁻²? =
  34. 34.What is the value of 2³ × 2⁻¹? =
  35. 35.Write 3¹¹ ÷ 3⁸ as a single power 3ⁿ. What is n?
  36. 36.What is the value of 3¹ × 3⁻⁴? =
  37. 37.Write 5¹⁴ ÷ 5⁵ as a single power 5ⁿ. What is n?
  38. 38.Write 6.5 × 10⁻¹ as a decimal. =
  39. 39.What is the value of (4/5)⁻¹? =
  40. 40.Write 7¹⁶ ÷ 7⁷ as a single power 7ⁿ. What is n?

Answer key

  1. 5
  2. 6600
  3. 0.00032
  4. 1/100
  5. 1/2
  6. 0.028
  7. 0.0098
  8. 1/2
  9. 1/729
  10. 64/49
  11. 72
  12. 512
  13. 17
  14. 0.0057
  15. 9
  16. 0.078
  17. 4
  18. 64
  19. 1/2
  20. 13
  21. 2
  22. 11
  23. 8/5
  24. 1
  25. 7/2
  26. 8/3
  27. 64
  28. 0.31
  29. 7
  30. 1296
  31. 3
  32. 3125
  33. 1/3
  34. 4
  35. 3
  36. 1/27
  37. 9
  38. 0.65
  39. 5/4
  40. 9

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