All work must be shown on all problems. Do not just write answers! (4 points each)

1. Simplify this, leaving no negative exponents:

((3a^-2b)^-3 (4ab^-3))/(6a⁷ b^-4c² )

2. Solve the below equation for x:

-5(w + 2x) = 3(ax + y) - q

3. Find the equation of the line in slope- intercept form that goes through (-2, 0) perpendicular to 3x - y = 6.

4. Solve (x-2)/(x+1)<2 . Graph the solution and give the answer in interval notation.

5. According to the Ministry of the Census, the population (in thousands) of yellow-throated flingas on Kinku Island can be approximated by p(x) = -.417x² + 43.368x + 250, where x = 0 corresponds to 1950. In what year did the Kinku Islands have the highest population of yellow-throated flingas? What was the population at that time?

6. Find vertical asymptote(s) and hole(s) for:

f(x)= (2x+1)/(2x²-5x-3)

7. Give the value of the discriminant and the number of real solutions for 3x + 2 = 2x² - 4x

8. Rationalize the denominator: (-2√5)/(3- √7)