(Solved): 1. Simplify and give your answer in radical form: \( \frac{x^{\frac{3}{4}}\left(x^{\frac{2}{3}}\rig ...

1. Simplify and give your answer in radical form: \( \frac{x^{\frac{3}{4}}\left(x^{\frac{2}{3}}\right)^{-\frac{3}{4}}}{x^{-\frac{1}{2}}} \) 2. Divide: \( \left(4 x^{4}-5 x^{2}\right) \div(5+2 x) \) 3. Factor completely: a. \( 10 x+3-8 x^{2} \) b. \( -x^{3}+3 x^{4}-12 x^{2}+4 x \) d. \( 16 x^{4}-81 y^{4} \) c. \( 32 x^{4}-108 x \) e. \( 6 x^{2}+47 x y-8 \) 4. Simplify: a. \( \frac{2 x-3}{x^{2}-5 x-6}-\frac{3 x-2}{x^{2}-36} \) b. \( \frac{3(x+1)+\left(x^{2}-4 x-5\right)}{(x+1)^{2}} \) C. \( \frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a+b}} \) 5. Rationalize the denominator: \( \frac{10}{\sqrt[3]{2 x^{2}}} \) 6. Rationalize the numerator: \( \frac{3 \sqrt{x}-5}{2 \sqrt{x}-3} \) 7. Solve the following equations exactly for \( x \) : a. \( 12 x^{2}=17 x-6 \) b. \( 5 x^{2}=6 x-4 \) c. \( x^{6}=6 x^{3}+16 \) (just the real solutions) d. \( |2 x-3|-7=4 \) e. \( \frac{3}{x-4}-\frac{5}{x+2}=\frac{18}{x^{2}-2 x-8} \) f. \( \frac{2 x-3}{2 x+1}=\frac{x-4}{x-5} \) g. \( \sqrt{5-x}-1=x \) h. \( e^{2 x+3}=12 \) i. \( 4 \ln (2 x+1)=10 \) j. \( \log (3 x+4)+\log (x-1)=\log (x+2) \) k. \( 2 x^{\frac{2}{3}}=4 \) 8. Solve the inequality \( |7 x-3| \geq 4 \). 9. Solve the inequality \( |7 x-3|<4 \). 10. Give, in slope-intercept form, the equation of the line through \( (-2,3) \) that perpendicular to the line \( 4 x-2 y=9 \).