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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 21 · 40 sums
TalentJR

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 3⁵ × 3⁻³? =
  2. 2.What is the value of 6⁵? =
  3. 3.What is the value of 2⁻⁴ (as a fraction)? =
  4. 4.What is the value of 2¹ × 2⁻⁶? =
  5. 5.2.4 × 10⁴ =
  6. 6.Write 6¹² ÷ 6⁶ as a single power 6ⁿ. What is n?
  7. 7.Write (5⁵)² as a single power 5ⁿ. What is n?
  8. 8.What is the value of 10⁴ × 10⁻³? =
  9. 9.What is the value of 2⁵ × 2⁻⁴? =
  10. 10.Write 3⁸ × 3⁹ as a single power 3ⁿ. What is n?
  11. 11.Write 45,000 in standard form as 4.5 × 10ⁿ. What is n?
  12. 12.What is the value of 3⁵ × 3⁻²? =
  13. 13.Write (3⁴)⁶ as a single power 3ⁿ. What is n?
  14. 14.What is the value of 2⁻³ (as a fraction)? =
  15. 15.What is the value of 3²? =
  16. 16.8.1 × 10⁶ =
  17. 17.Write (4³)⁶ as a single power 4ⁿ. What is n?
  18. 18.Write 64,000 in standard form as 6.4 × 10ⁿ. What is n?
  19. 19.8.1 × 10⁷ =
  20. 20.Write 4¹² ÷ 4³ as a single power 4ⁿ. What is n?
  21. 21.Write 4,00,000 in standard form as 4 × 10ⁿ. What is n?
  22. 22.Write 55,00,000 in standard form as 5.5 × 10ⁿ. What is n?
  23. 23.What is the value of 9³? =
  24. 24.What is the value of 3⁴? =
  25. 25.What is the value of 6⁴? =
  26. 26.What is the value of 3⁵ × 3⁻¹? =
  27. 27.4.5 × 10³ =
  28. 28.3.3 × 10⁷ =
  29. 29.What is the value of (1/7)⁻²? =
  30. 30.Write (7⁸)³ as a single power 7ⁿ. What is n?
  31. 31.What is the value of 2¹ × 2⁻⁵? =
  32. 32.What is the value of 2¹⁶? =
  33. 33.Write (7⁷)⁹ as a single power 7ⁿ. What is n?
  34. 34.What is the value of 3⁴ × 3⁻⁴? =
  35. 35.1.1 × 10⁷ =
  36. 36.Write 4,000 in standard form as 4 × 10ⁿ. What is n?
  37. 37.What is the value of 2³ × 2⁻¹? =
  38. 38.Write (9⁹)⁴ as a single power 9ⁿ. What is n?
  39. 39.What is the value of 3⁵? =
  40. 40.Write 84,00,000 in standard form as 8.4 × 10ⁿ. What is n?

Answer key

  1. 9
  2. 7776
  3. 1/16
  4. 1/32
  5. 24000
  6. 6
  7. 10
  8. 10
  9. 2
  10. 17
  11. 4
  12. 27
  13. 24
  14. 1/8
  15. 9
  16. 8100000
  17. 18
  18. 4
  19. 81000000
  20. 9
  21. 5
  22. 6
  23. 729
  24. 81
  25. 1296
  26. 81
  27. 4500
  28. 33000000
  29. 49
  30. 24
  31. 1/16
  32. 65536
  33. 63
  34. 1
  35. 11000000
  36. 3
  37. 4
  38. 36
  39. 243
  40. 6

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