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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 179 · 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 2⁻³ (as a fraction)? =
  2. 2.What is the value of (5/7)⁻¹? =
  3. 3.What is the value of 5² × 5⁻²? =
  4. 4.Write 1.5 × 10⁻² as a decimal. =
  5. 5.Write 5.9 × 10⁻¹ as a decimal. =
  6. 6.Write 7⁵ × 7⁶ as a single power 7ⁿ. What is n?
  7. 7.What is the value of (2/5)⁻¹? =
  8. 8.What is the value of 6⁻³ (as a fraction)? =
  9. 9.What is the value of 2⁶ × 2⁻⁶? =
  10. 10.Write 7.4 × 10⁻¹ as a decimal. =
  11. 11.What is the value of 2⁴ × 2⁻⁴? =
  12. 12.Write 7.3 × 10⁻⁴ as a decimal. =
  13. 13.What is the value of 2¹¹? =
  14. 14.Write 7.5 × 10⁻³ as a decimal. =
  15. 15.Write 8.6 × 10⁻¹ as a decimal. =
  16. 16.What is the value of 10² × 10⁻²? =
  17. 17.Write 9,50,000 in standard form as 9.5 × 10ⁿ. What is n?
  18. 18.Write 30,00,000 in standard form as 3 × 10ⁿ. What is n?
  19. 19.Write 6⁷ ÷ 6³ as a single power 6ⁿ. What is n?
  20. 20.Write 3¹¹ ÷ 3⁸ as a single power 3ⁿ. What is n?
  21. 21.Write 4.2 × 10⁻⁴ as a decimal. =
  22. 22.What is the value of (8/9)⁻²? =
  23. 23.What is the value of 10⁴ × 10⁻³? =
  24. 24.Write 3 × 10⁻¹ as a decimal. =
  25. 25.Write 55,000 in standard form as 5.5 × 10ⁿ. What is n?
  26. 26.Write 2⁸ ÷ 2⁵ as a single power 2ⁿ. What is n?
  27. 27.What is the value of (2/3)⁻¹? =
  28. 28.What is the value of 2¹⁶? =
  29. 29.What is the value of 2³? =
  30. 30.9.8 × 10⁴ =
  31. 31.Write 9³ × 9⁴ as a single power 9ⁿ. What is n?
  32. 32.What is the value of 2⁻⁵ (as a fraction)? =
  33. 33.What is the value of 3² × 3⁻⁴? =
  34. 34.2.6 × 10⁶ =
  35. 35.Write 6 × 10⁻¹ as a decimal. =
  36. 36.2.2 × 10² =
  37. 37.Write 4.3 × 10⁻³ as a decimal. =
  38. 38.Write (4³)² as a single power 4ⁿ. What is n?
  39. 39.What is the value of 2¹²? =
  40. 40.What is the value of 3⁷? =

Answer key

  1. 1/8
  2. 7/5
  3. 1
  4. 0.015
  5. 0.59
  6. 11
  7. 5/2
  8. 1/216
  9. 1
  10. 0.74
  11. 1
  12. 0.00073
  13. 2048
  14. 0.0075
  15. 0.86
  16. 1
  17. 5
  18. 6
  19. 4
  20. 3
  21. 0.00042
  22. 81/64
  23. 10
  24. 0.3
  25. 4
  26. 3
  27. 3/2
  28. 65536
  29. 8
  30. 98000
  31. 7
  32. 1/32
  33. 1/9
  34. 2600000
  35. 0.6
  36. 220
  37. 0.0043
  38. 6
  39. 4096
  40. 2187

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