5. Simplifica a la menor expresión las siguientes potencias: a. \( \frac{2^{3} 3^{3} 30^{2} 5^{3}}{3^{6} 30^{3} 5^{2}} \) b. \( \frac{2^{3} 4^{3} 10^{3} 3^{4} 4^{3}}{3^{6} 4^{3} 10^{2}} \)

Solve the equation by factoring. Select the correct solution. \( 6 x^{2}-5 x-4=0 \) \( \begin{array}{ll}\text { O } & \text { A) } x=-\frac{4}{3},-\frac{1}{2} \\ \text { O } & \text { B) } x=-\frac{1}{2}, \frac{4}{3} \\ \text { O } & \text { C) } x=-\frac{4}{3}, \frac{1}{2} \\ \text { - } & \text { D) } x=\frac{1}{2}, \frac{4}{3}\end{array} \)

1. Louls owns his own orchard. He plants 5 fruit trees for every 5 nut tiees. The equation \( f=\frac{9}{5} n \) models the relationship between the number of nut trees planted and the number of fruit trees planted. Determine the number of nut trees planted if 135 fruit trees were planted.

Consider the line \( y=\frac{5}{2} x-3 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (2,-5) \). Find the equation of the line that is parallel to this line and passes through the point (2, -5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line:

1 Graph \( y-2=\frac{2}{3}(x-3) \)

Write in exponential form. \[ \log _{6} 216=3 \] Write the equivalent exponential equation. \( \square \) (Type an equation. Type your answer using expc