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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 678 · 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 7⁴? =
  2. 2.Write 4⁵ × 4³ as a single power 4ⁿ. What is n?
  3. 3.Write 6⁹ ÷ 6⁶ as a single power 6ⁿ. What is n?
  4. 4.Write 4 × 10⁻² as a decimal. =
  5. 5.Write 4,60,000 in standard form as 4.6 × 10ⁿ. What is n?
  6. 6.Write 5¹⁴ ÷ 5⁷ as a single power 5ⁿ. What is n?
  7. 7.What is the value of 9⁵? =
  8. 8.Write (8²)⁵ as a single power 8ⁿ. What is n?
  9. 9.What is the value of 3⁻⁴ (as a fraction)? =
  10. 10.What is the value of 5³ × 5⁻²? =
  11. 11.2.5 × 10⁷ =
  12. 12.Write 7,20,00,000 in standard form as 7.2 × 10ⁿ. What is n?
  13. 13.Write 3.5 × 10⁻¹ as a decimal. =
  14. 14.What is the value of 2⁻⁹ (as a fraction)? =
  15. 15.8.8 × 10⁶ =
  16. 16.What is the value of (3/8)⁻²? =
  17. 17.What is the value of 2⁷? =
  18. 18.Write 2.9 × 10⁻³ as a decimal. =
  19. 19.What is the value of 2⁴ × 2⁻⁵? =
  20. 20.Write 4⁴ × 4³ as a single power 4ⁿ. What is n?
  21. 21.Write 2.9 × 10⁻² as a decimal. =
  22. 22.What is the value of 2² × 2⁻⁵? =
  23. 23.What is the value of 2¹ × 2⁻⁵? =
  24. 24.What is the value of 5³ × 5⁻³? =
  25. 25.What is the value of 2² × 2⁻⁴? =
  26. 26.3.1 × 10⁴ =
  27. 27.Write 7.7 × 10⁻² as a decimal. =
  28. 28.6.1 × 10⁷ =
  29. 29.Write 2.8 × 10⁻¹ as a decimal. =
  30. 30.What is the value of 2⁴ × 2⁻¹? =
  31. 31.What is the value of 3¹ × 3⁻⁵? =
  32. 32.What is the value of 3² × 3⁻²? =
  33. 33.What is the value of 4⁻³ (as a fraction)? =
  34. 34.2.1 × 10³ =
  35. 35.What is the value of 5⁶? =
  36. 36.What is the value of (4/7)⁻¹? =
  37. 37.What is the value of (5/8)⁻²? =
  38. 38.Write 8⁷ × 8⁹ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 4⁶? =
  40. 40.Write 1,600 in standard form as 1.6 × 10ⁿ. What is n?

Answer key

  1. 2401
  2. 8
  3. 3
  4. 0.04
  5. 5
  6. 7
  7. 59049
  8. 10
  9. 1/81
  10. 5
  11. 25000000
  12. 7
  13. 0.35
  14. 1/512
  15. 8800000
  16. 64/9
  17. 128
  18. 0.0029
  19. 1/2
  20. 7
  21. 0.029
  22. 1/8
  23. 1/16
  24. 1
  25. 1/4
  26. 31000
  27. 0.077
  28. 61000000
  29. 0.28
  30. 8
  31. 1/81
  32. 1
  33. 1/64
  34. 2100
  35. 15625
  36. 7/4
  37. 64/25
  38. 16
  39. 4096
  40. 3

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