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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 616 · 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 4⁻² (as a fraction)? =
  2. 2.What is the value of (1/6)⁻²? =
  3. 3.What is the value of 3⁵ × 3⁻¹? =
  4. 4.Write 1.5 × 10⁻³ as a decimal. =
  5. 5.2.4 × 10² =
  6. 6.Write 5⁹ × 5⁷ as a single power 5ⁿ. What is n?
  7. 7.Write 99,000 in standard form as 9.9 × 10ⁿ. What is n?
  8. 8.What is the value of 2²? =
  9. 9.What is the value of (1/9)⁻²? =
  10. 10.What is the value of (5/9)⁻¹? =
  11. 11.What is the value of 9⁻² (as a fraction)? =
  12. 12.What is the value of 5⁶ × 5⁻³? =
  13. 13.Write 1,600 in standard form as 1.6 × 10ⁿ. What is n?
  14. 14.What is the value of 10⁴ × 10⁻¹? =
  15. 15.Write 5.9 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of (2/5)⁻¹? =
  17. 17.1.3 × 10² =
  18. 18.What is the value of (3/4)⁻²? =
  19. 19.What is the value of 3⁴? =
  20. 20.Write 280 in standard form as 2.8 × 10ⁿ. What is n?
  21. 21.What is the value of 10² × 10⁻¹? =
  22. 22.What is the value of 2¹²? =
  23. 23.What is the value of 10¹ × 10⁻⁶? =
  24. 24.What is the value of 6⁶? =
  25. 25.Write 7,80,000 in standard form as 7.8 × 10ⁿ. What is n?
  26. 26.Write 3,20,00,000 in standard form as 3.2 × 10ⁿ. What is n?
  27. 27.What is the value of 2⁹? =
  28. 28.What is the value of 9⁵? =
  29. 29.Write 3¹⁶ ÷ 3⁹ as a single power 3ⁿ. What is n?
  30. 30.Write (8⁹)⁹ as a single power 8ⁿ. What is n?
  31. 31.Write (5⁶)⁸ as a single power 5ⁿ. What is n?
  32. 32.What is the value of 7³? =
  33. 33.Write 9¹⁴ ÷ 9⁹ as a single power 9ⁿ. What is n?
  34. 34.Write 5.5 × 10⁻¹ as a decimal. =
  35. 35.Write 24,00,000 in standard form as 2.4 × 10ⁿ. What is n?
  36. 36.2.9 × 10⁷ =
  37. 37.Write 6¹⁴ ÷ 6⁷ as a single power 6ⁿ. What is n?
  38. 38.1.7 × 10⁷ =
  39. 39.What is the value of (2/9)⁻¹? =
  40. 40.Write 2.6 × 10⁻³ as a decimal. =

Answer key

  1. 1/16
  2. 36
  3. 81
  4. 0.0015
  5. 240
  6. 16
  7. 4
  8. 4
  9. 81
  10. 9/5
  11. 1/81
  12. 125
  13. 3
  14. 1000
  15. 0.00059
  16. 5/2
  17. 130
  18. 16/9
  19. 81
  20. 2
  21. 10
  22. 4096
  23. 1/100000
  24. 46656
  25. 5
  26. 7
  27. 512
  28. 59049
  29. 7
  30. 81
  31. 48
  32. 343
  33. 5
  34. 0.55
  35. 6
  36. 29000000
  37. 7
  38. 17000000
  39. 9/2
  40. 0.0026

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