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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 786 · 40 sums
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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.What is the value of 2⁻⁴ (as a fraction)? =
  2. 2.Write 4.3 × 10⁻⁴ as a decimal. =
  3. 3.What is the value of 3¹ × 3⁻⁶? =
  4. 4.Write (6⁸)³ as a single power 6ⁿ. What is n?
  5. 5.What is the value of 2¹⁶? =
  6. 6.Write 4¹⁰ ÷ 4⁶ as a single power 4ⁿ. What is n?
  7. 7.What is the value of 10⁶ × 10⁻⁶? =
  8. 8.What is the value of (4/7)⁻¹? =
  9. 9.Write 4⁷ ÷ 4⁴ as a single power 4ⁿ. What is n?
  10. 10.What is the value of 5⁻¹ (as a fraction)? =
  11. 11.Write 4.9 × 10⁻² as a decimal. =
  12. 12.What is the value of (5/6)⁻¹? =
  13. 13.What is the value of 5² × 5⁻⁵? =
  14. 14.1.1 × 10⁵ =
  15. 15.What is the value of 3⁶? =
  16. 16.3.3 × 10⁵ =
  17. 17.Write (8³)⁸ as a single power 8ⁿ. What is n?
  18. 18.What is the value of 7⁻¹ (as a fraction)? =
  19. 19.What is the value of 5⁻² (as a fraction)? =
  20. 20.What is the value of 10² × 10⁻⁴? =
  21. 21.What is the value of 6⁵? =
  22. 22.Write 75,00,000 in standard form as 7.5 × 10ⁿ. What is n?
  23. 23.Write 2.8 × 10⁻⁴ as a decimal. =
  24. 24.Write 8 × 10⁻³ as a decimal. =
  25. 25.What is the value of 3⁵ × 3⁻²? =
  26. 26.What is the value of 3¹ × 3⁻⁵? =
  27. 27.What is the value of 3⁶ × 3⁻¹? =
  28. 28.What is the value of 3¹⁰? =
  29. 29.What is the value of 10¹ × 10⁻³? =
  30. 30.What is the value of 4⁴? =
  31. 31.Write 96,000 in standard form as 9.6 × 10ⁿ. What is n?
  32. 32.3.4 × 10² =
  33. 33.What is the value of 3⁻⁴ (as a fraction)? =
  34. 34.What is the value of (1/9)⁻¹? =
  35. 35.What is the value of 10² × 10⁻³? =
  36. 36.Write (9⁶)⁸ as a single power 9ⁿ. What is n?
  37. 37.What is the value of 3⁻¹ (as a fraction)? =
  38. 38.5.9 × 10⁶ =
  39. 39.What is the value of 3¹ × 3⁻²? =
  40. 40.Write 3² × 3⁵ as a single power 3ⁿ. What is n?

Answer key

  1. 1/16
  2. 0.00043
  3. 1/243
  4. 24
  5. 65536
  6. 4
  7. 1
  8. 7/4
  9. 3
  10. 1/5
  11. 0.049
  12. 6/5
  13. 1/125
  14. 110000
  15. 729
  16. 330000
  17. 24
  18. 1/7
  19. 1/25
  20. 1/100
  21. 7776
  22. 6
  23. 0.00028
  24. 0.008
  25. 27
  26. 1/81
  27. 243
  28. 59049
  29. 1/100
  30. 256
  31. 4
  32. 340
  33. 1/81
  34. 9
  35. 1/10
  36. 48
  37. 1/3
  38. 5900000
  39. 1/3
  40. 7

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