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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 160 · 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 5² × 5⁻⁵? =
  2. 2.What is the value of 3⁵ × 3⁻²? =
  3. 3.What is the value of 10⁴? =
  4. 4.What is the value of 2⁴ × 2⁻⁴? =
  5. 5.7.6 × 10⁷ =
  6. 6.What is the value of 4³? =
  7. 7.What is the value of 10²? =
  8. 8.What is the value of 5⁴? =
  9. 9.What is the value of 4⁻¹ (as a fraction)? =
  10. 10.What is the value of 2¹²? =
  11. 11.What is the value of 2⁻⁹ (as a fraction)? =
  12. 12.Write (9⁵)⁸ as a single power 9ⁿ. What is n?
  13. 13.1.6 × 10⁷ =
  14. 14.What is the value of 3⁻⁶ (as a fraction)? =
  15. 15.What is the value of (2/9)⁻²? =
  16. 16.What is the value of 7⁻¹ (as a fraction)? =
  17. 17.What is the value of 7²? =
  18. 18.What is the value of 2⁸? =
  19. 19.What is the value of (6/7)⁻²? =
  20. 20.Write 4.8 × 10⁻⁴ as a decimal. =
  21. 21.What is the value of 3³ × 3⁻⁴? =
  22. 22.What is the value of 3²? =
  23. 23.Write 1.7 × 10⁻³ as a decimal. =
  24. 24.Write 9.6 × 10⁻² as a decimal. =
  25. 25.Write 6⁶ × 6³ as a single power 6ⁿ. What is n?
  26. 26.Write 2,700 in standard form as 2.7 × 10ⁿ. What is n?
  27. 27.Write 72,000 in standard form as 7.2 × 10ⁿ. What is n?
  28. 28.Write 7⁹ × 7⁹ as a single power 7ⁿ. What is n?
  29. 29.What is the value of (1/3)⁻¹? =
  30. 30.What is the value of 5³ × 5⁻⁵? =
  31. 31.What is the value of 2⁴ × 2⁻³? =
  32. 32.Write 1.4 × 10⁻¹ as a decimal. =
  33. 33.What is the value of 3⁸? =
  34. 34.Write 3.9 × 10⁻³ as a decimal. =
  35. 35.What is the value of 6⁻¹ (as a fraction)? =
  36. 36.What is the value of 5³ × 5⁻¹? =
  37. 37.Write 7⁸ ÷ 7⁵ as a single power 7ⁿ. What is n?
  38. 38.Write 5⁸ ÷ 5² as a single power 5ⁿ. What is n?
  39. 39.Write 130 in standard form as 1.3 × 10ⁿ. What is n?
  40. 40.Write 210 in standard form as 2.1 × 10ⁿ. What is n?

Answer key

  1. 1/125
  2. 27
  3. 10000
  4. 1
  5. 76000000
  6. 64
  7. 100
  8. 625
  9. 1/4
  10. 4096
  11. 1/512
  12. 40
  13. 16000000
  14. 1/729
  15. 81/4
  16. 1/7
  17. 49
  18. 256
  19. 49/36
  20. 0.00048
  21. 1/3
  22. 9
  23. 0.0017
  24. 0.096
  25. 9
  26. 3
  27. 4
  28. 18
  29. 3
  30. 1/25
  31. 2
  32. 0.14
  33. 6561
  34. 0.0039
  35. 1/6
  36. 25
  37. 3
  38. 6
  39. 2
  40. 2

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