1. Simplify the expression using properties of exponents. Answer should contain positive exponents only.
(3x^2y^3)^2(3xy)^2 / (2x^4y^3)^-3
2. Solve for X:
3/x - 1/x+2 = -2/3x+6
3. Use the quadratic formula to solve for x:
x^2 -4x + 2 = 0
4. Solve for x by factoring:
x^3 + x^2 - 6x = 0
5. Factor completely:
X^4y^2 - x^4 - 5y^2 + 5
For Questions 6 -11, refer to the following functions:
f(x) = x^2 - 6 g(x) = 3x + 2 h(x) = x - 4 / x^2 - 64
6. Find f(x) * g(x)
7. What is the domain of h(x) ?
8. Find f(g(x))
9. Find h(-4)
10. Find the inverse of g(x)
11. Give the equations of any horizontal or vertical asymptotes of h(x)
3x - 4 = 12
13. Find the equation of the line passing through the points (6,-1) and (5,2). Write answer in slope-intercept form.
14. Find the equation of the line passing through the point (-3,10) that is perpendicular to the line y =-3/2x + 4. Write answer in slope-intercept form.
F(x) = 4(x + 3)^2 -4
16. Use long division to divide:
5x^3-6x^2-28x-2 by x + 2
17. Write the equation of the circle with center (2,-5) and radius 3,and graph the circle.
18. Solve the following inequality for x:
-10 is less than or equal to 2 - 4x is less than or equal to 10
This solution is comprised of a detailed explanation to simplify the expression using properties of exponents.