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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 812 · 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 2⁴ × 2⁻¹? =
  2. 2.Write 4.6 × 10⁻⁴ as a decimal. =
  3. 3.Write (5⁸)⁸ as a single power 5ⁿ. What is n?
  4. 4.What is the value of 8⁻² (as a fraction)? =
  5. 5.What is the value of 10⁴ × 10⁻³? =
  6. 6.Write (5⁵)⁹ as a single power 5ⁿ. What is n?
  7. 7.Write 82,00,000 in standard form as 8.2 × 10ⁿ. What is n?
  8. 8.Write 2¹⁰ ÷ 2⁵ as a single power 2ⁿ. What is n?
  9. 9.3.9 × 10² =
  10. 10.What is the value of 6⁻¹ (as a fraction)? =
  11. 11.Write 1,70,000 in standard form as 1.7 × 10ⁿ. What is n?
  12. 12.Write 8,700 in standard form as 8.7 × 10ⁿ. What is n?
  13. 13.What is the value of (4/5)⁻¹? =
  14. 14.Write 170 in standard form as 1.7 × 10ⁿ. What is n?
  15. 15.What is the value of 5⁶ × 5⁻⁵? =
  16. 16.What is the value of 2¹⁰? =
  17. 17.What is the value of 3⁷? =
  18. 18.What is the value of 5⁴ × 5⁻⁴? =
  19. 19.Write 250 in standard form as 2.5 × 10ⁿ. What is n?
  20. 20.What is the value of 2⁵ × 2⁻⁶? =
  21. 21.What is the value of 6⁴? =
  22. 22.Write 7¹¹ ÷ 7³ as a single power 7ⁿ. What is n?
  23. 23.Write 2¹⁴ ÷ 2⁷ as a single power 2ⁿ. What is n?
  24. 24.6 × 10² =
  25. 25.What is the value of 2⁻⁴ (as a fraction)? =
  26. 26.What is the value of 2³ × 2⁻⁶? =
  27. 27.What is the value of 2¹ × 2⁻²? =
  28. 28.What is the value of 5² × 5⁻³? =
  29. 29.What is the value of 2⁻¹ (as a fraction)? =
  30. 30.Write 2.7 × 10⁻³ as a decimal. =
  31. 31.What is the value of 10² × 10⁻⁶? =
  32. 32.Write 3¹⁴ ÷ 3⁷ as a single power 3ⁿ. What is n?
  33. 33.What is the value of 4⁻¹ (as a fraction)? =
  34. 34.What is the value of 2⁻⁵ (as a fraction)? =
  35. 35.What is the value of (4/9)⁻¹? =
  36. 36.What is the value of 2⁴ × 2⁻⁵? =
  37. 37.What is the value of 10² × 10⁻⁵? =
  38. 38.What is the value of 2⁻⁶ (as a fraction)? =
  39. 39.Write 5¹² ÷ 5⁶ as a single power 5ⁿ. What is n?
  40. 40.Write 6³ × 6⁸ as a single power 6ⁿ. What is n?

Answer key

  1. 8
  2. 0.00046
  3. 64
  4. 1/64
  5. 10
  6. 45
  7. 6
  8. 5
  9. 390
  10. 1/6
  11. 5
  12. 3
  13. 5/4
  14. 2
  15. 5
  16. 1024
  17. 2187
  18. 1
  19. 2
  20. 1/2
  21. 1296
  22. 8
  23. 7
  24. 600
  25. 1/16
  26. 1/8
  27. 1/2
  28. 1/5
  29. 1/2
  30. 0.0027
  31. 1/10000
  32. 7
  33. 1/4
  34. 1/32
  35. 9/4
  36. 1/2
  37. 1/1000
  38. 1/64
  39. 6
  40. 11

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