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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 783 · 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.Write 59,00,000 in standard form as 5.9 × 10ⁿ. What is n?
  2. 2.What is the value of 4⁻² (as a fraction)? =
  3. 3.Write 3⁸ × 3⁵ as a single power 3ⁿ. What is n?
  4. 4.What is the value of 2¹²? =
  5. 5.What is the value of 2⁻³ (as a fraction)? =
  6. 6.What is the value of 8⁻¹ (as a fraction)? =
  7. 7.What is the value of 2⁻⁴ (as a fraction)? =
  8. 8.Write 2.2 × 10⁻⁴ as a decimal. =
  9. 9.What is the value of (4/7)⁻¹? =
  10. 10.What is the value of 2⁴ × 2⁻⁶? =
  11. 11.What is the value of 7³? =
  12. 12.Write 5,200 in standard form as 5.2 × 10ⁿ. What is n?
  13. 13.What is the value of (1/3)⁻¹? =
  14. 14.Write 21,00,000 in standard form as 2.1 × 10ⁿ. What is n?
  15. 15.What is the value of 3⁻³ (as a fraction)? =
  16. 16.What is the value of 5⁵ × 5⁻¹? =
  17. 17.Write 5,80,00,000 in standard form as 5.8 × 10ⁿ. What is n?
  18. 18.Write 4.7 × 10⁻¹ as a decimal. =
  19. 19.What is the value of 4⁷? =
  20. 20.Write 1.8 × 10⁻³ as a decimal. =
  21. 21.Write 6⁹ × 6⁷ as a single power 6ⁿ. What is n?
  22. 22.8.9 × 10⁵ =
  23. 23.What is the value of 3¹⁰? =
  24. 24.What is the value of 10¹ × 10⁻³? =
  25. 25.What is the value of 2¹⁴? =
  26. 26.Write 8.4 × 10⁻¹ as a decimal. =
  27. 27.Write 2⁴ × 2⁶ as a single power 2ⁿ. What is n?
  28. 28.What is the value of 3²? =
  29. 29.Write 9¹³ ÷ 9⁷ as a single power 9ⁿ. What is n?
  30. 30.What is the value of (3/4)⁻²? =
  31. 31.What is the value of 2⁷? =
  32. 32.Write 540 in standard form as 5.4 × 10ⁿ. What is n?
  33. 33.What is the value of 6⁵? =
  34. 34.Write 5⁸ ÷ 5⁵ as a single power 5ⁿ. What is n?
  35. 35.What is the value of (1/6)⁻²? =
  36. 36.What is the value of 5¹ × 5⁻⁴? =
  37. 37.What is the value of 5³ × 5⁻¹? =
  38. 38.Write 8⁴ × 8⁶ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 9⁻³ (as a fraction)? =
  40. 40.What is the value of (1/4)⁻²? =

Answer key

  1. 6
  2. 1/16
  3. 13
  4. 4096
  5. 1/8
  6. 1/8
  7. 1/16
  8. 0.00022
  9. 7/4
  10. 1/4
  11. 343
  12. 3
  13. 3
  14. 6
  15. 1/27
  16. 625
  17. 7
  18. 0.47
  19. 16384
  20. 0.0018
  21. 16
  22. 890000
  23. 59049
  24. 1/100
  25. 16384
  26. 0.84
  27. 10
  28. 9
  29. 6
  30. 16/9
  31. 128
  32. 2
  33. 7776
  34. 3
  35. 36
  36. 1/125
  37. 25
  38. 10
  39. 1/729
  40. 16

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