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UST Middle School Algebra I Challenge

Week 8 — Exponents & Exponential Expressions

Focus: Exponent rules, zero/negative exponents, growth

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Weekly Format

Week 8

Part A — 15 Multiple Choice

Part B — 15 Fill in the Blank

Part C — 15 Word / Open-Response Problems

Part D — 5 Challenge Problems

Answer key and step-by-step explanations follow the questions.

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Part A — Multiple Choice

Questions 1–5

1. Simplify x³·x^3. A) x^6 B) x^9 C) x^0 D) 3x³

2. Simplify x³·x^4. A) x^7 B) x^12 C) x^1 D) 4x³

3. Simplify x³·x^5. A) x^8 B) x^15 C) x^2 D) 5x³

4. Simplify x³·x^2. A) x^5 B) x^6 C) x^-1 D) 2x³

5. Simplify x³·x^3. A) x^6 B) x^9 C) x^0 D) 3x³

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Part A — Multiple Choice

Questions 6–10

6. Simplify x³·x^4. A) x^7 B) x^12 C) x^1 D) 4x³

7. Simplify x³·x^5. A) x^8 B) x^15 C) x^2 D) 5x³

8. Simplify x³·x^2. A) x^5 B) x^6 C) x^-1 D) 2x³

9. Simplify x³·x^3. A) x^6 B) x^9 C) x^0 D) 3x³

10. Simplify x³·x^4. A) x^7 B) x^12 C) x^1 D) 4x³

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Part A — Multiple Choice

Questions 11–15

11. Simplify x³·x^5. A) x^8 B) x^15 C) x^2 D) 5x³

12. Simplify x³·x^2. A) x^5 B) x^6 C) x^-1 D) 2x³

13. Simplify x³·x^3. A) x^6 B) x^9 C) x^0 D) 3x³

14. Simplify x³·x^4. A) x^7 B) x^12 C) x^1 D) 4x³

15. Simplify x³·x^5. A) x^8 B) x^15 C) x^2 D) 5x³

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Part B — Fill in the Blank

Questions 16–20

16. Simplify (a²)^2: ___.

17. Simplify (a²)^3: ___.

18. Simplify (a²)^4: ___.

19. Simplify (a²)^5: ___.

20. Simplify (a²)^6: ___.

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Part B — Fill in the Blank

Questions 21–25

21. Simplify (a²)^7: ___.

22. Simplify (a²)^8: ___.

23. Simplify (a²)^9: ___.

24. Simplify (a²)^10: ___.

25. Simplify (a²)^11: ___.

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Part B — Fill in the Blank

Questions 26–30

26. Simplify (a²)^12: ___.

27. Simplify (a²)^13: ___.

28. Simplify (a²)^14: ___.

29. Simplify (a²)^15: ___.

30. Simplify (a²)^16: ___.

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Part C — Word / Open Response

Questions 31–35

31. A quantity starts at 5 and doubles 4 times. Find the final amount.

32. A quantity starts at 6 and doubles 4 times. Find the final amount.

33. A quantity starts at 7 and doubles 4 times. Find the final amount.

34. A quantity starts at 8 and doubles 4 times. Find the final amount.

35. A quantity starts at 9 and doubles 4 times. Find the final amount.

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Part C — Word / Open Response

Questions 36–40

36. A quantity starts at 10 and doubles 4 times. Find the final amount.

37. A quantity starts at 11 and doubles 4 times. Find the final amount.

38. A quantity starts at 12 and doubles 4 times. Find the final amount.

39. A quantity starts at 13 and doubles 4 times. Find the final amount.

40. A quantity starts at 14 and doubles 4 times. Find the final amount.

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Part C — Word / Open Response

Questions 41–45

41. A quantity starts at 15 and doubles 4 times. Find the final amount.

42. A quantity starts at 16 and doubles 4 times. Find the final amount.

43. A quantity starts at 17 and doubles 4 times. Find the final amount.

44. A quantity starts at 18 and doubles 4 times. Find the final amount.

45. A quantity starts at 19 and doubles 4 times. Find the final amount.

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Part D — Challenge

Questions 46–50

46. Challenge: Simplify (x⁵/x²)·x^2.

47. Challenge: Simplify (x⁵/x²)·x^3.

48. Challenge: Simplify (x⁵/x²)·x^4.

49. Challenge: Simplify (x⁵/x²)·x^5.

50. Challenge: Simplify (x⁵/x²)·x^6.

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Answer Key — Questions 1–5

Answer + How to Solve

1. Answer: A