# Simplifying and Solving Equations with Exponents

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)

12. State the slope and y-intercept of the line given below and graph the line on the axis.

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.

15. Find the vertex and x-intercepts of the function given below and graph the parabola.

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.

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#### Solution Summary

This solution is comprised of a detailed explanation to simplify the expression using properties of exponents.