1. The velocity $v$ (in ft/sec) after falling $d$ feet is estimated by $v = \sqrt{64d}$. What is the velocity after falling 25 feet?
2. Let $P(t) = 400(3)^{\frac{t}{2}}$. What is the value of $P(6)$?
3. If $x^{\frac{2}{3}} = 16$ and $x > 0$, what is the value of $x$?
4. Given $\sqrt6{x} \= y$ where $y$ is a real number, what must be true of $x$?
5. What is $4^3$?
6. Which expression equals $e^{-5}$?
7. Simplify: $\sqrt{27}$
8. What is the value of $x$ if $2^x=32$?
9. Simplify: $ (x^3)^4 $
10. What is the domain of the real-valued function $f(x) = \sqrt{x - 5}$?
11. Simplify: $\sqrt{75}$
12. Which of the following values is closest to $4 \cdot 10^3 + 3 \cdot 10^{-2}$
13. Given the function $f(x) = \sqrt<u>4</u>{x - 5}$, what is the domain of $f(x)$ in the real number system?
14. If $x$ and $y$ are positive integers such that $3^x \cdot 3^y = 81$, what is the greatest possible value of $x - y$?
15. If $\sqrt{2x + 5} = 3$, what is the value of $x$?
16. For the function $f(x) = \dfrac{2x - 5}{3}$, which of the following defines its inverse function $f^{-1}(x)$?
17. Simplify: $\sqrt{50}$
18. What is $7^{-1}$?
19. Which expression equals $c^{-1}$?
20. Simplify: $\sqrt{32}$
21. Simplify: $\sqrt{12}$
22. Which expression equals $a^{-3}$?
23. Simplify: $\sqrt{98}$
24. What is $8^0$?
25. What is $11^0$?
26. What is $3^4$?
27. What is $6^2$?
28. Simplify: $\sqrt{20}$
29. Simplify: $\sqrt{12}\cdot\sqrt{3}$
30. Simplify: $\dfrac{\sqrt{48}}{\sqrt{3}}$
31. What is $(-2)^4$?
32. Simplify: $\dfrac{5^6}{5^2}$
33. Simplify: $\dfrac{2^{-3}}{2^{-5}}$
34. A quantity decreases by a factor of $\left(\dfrac{1}{2}\right)$ each hour. Which expression gives the quantity after $t$ hours if it starts at $64$?
35. Which expression equals $a^{-4}$ (for $a\ne 0$)?
36. Apply exponent rules to simplify: $2^3\cdot 2^5$
37. Simplify: $\sqrt{27y^2}$, assuming $y \ge 0$.
38. What is $4^{3/2}$?
39. What is the value of $x$ if $5^{x}=\dfrac{1}{25}$?
40. Apply exponent rules to simplify: $\left(\dfrac{1}{3}\right)^{-2}$
41. The period $T$, in seconds, of a pendulum is given by the formula $T = 2\pi\sqrt{\frac{L}{9.8}}$, where $L$ is the length of the pendulum in meters. Approximately what is the period, in seconds, of a pendulum with a length of 2.45 meters?
42. What is $3^{-2}$?
43. What is $12^1$?
44. What is $13^{-1}$?
45. Simplify: $\sqrt{72}$
46. Simplify: $\sqrt{44}$
47. Which expression equals $b^{-2}$?
48. Simplify: $\sqrt{18}$
49. What is $9^{-2}$?
50. Simplify: $\sqrt{45}$
51. Simplify: $\sqrt{200}$
52. What is $2^{-3}$?
53. Which expression equals $f^{-6}$?
54. What is $5^{-2}$?
55. What is $10^1$?
56. Simplify: $\sqrt{128}$
57. Simplify: $\sqrt{18x^2}$, assuming $x\ge 0$.
58. Which expression equals $d^{-4}$?
59. If $x$ and $y$ are positive integers such that $3^x \cdot 3^y = 81$, what is the greatest possible value of $x - y$?
60. If $\sqrt{2x + 5} = 3$, what is the value of $x$?