Aşağıda verilen eşitliklerden hangisi yanlıştır? \( \begin{array}{ll}\text { A) } 3^{4} \cdot 3^{-5}=\frac{1}{3} & \text { B) } 2^{5} \cdot 3^{5}=6^{5} \\ \text { C) } \frac{15^{6}}{5^{6}}=3^{6} & \text { D) } \frac{5^{12}}{5^{4}}=5^{3}\end{array} \)

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

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:

Use the properties of logarithms to rewrite the expression. Simplify the res \( \log _{3} \frac{\sqrt{x} \sqrt[3]{y}}{w} \sqrt{z} \) Choose the correct answer. A. \( -\frac{1}{2} \log _{3} x-\frac{1}{3} \log _{3} y+5 \log _{3} w+\frac{1}{2} \log _{3} z \) B. \( \frac{1}{2} \log _{3} x+\frac{1}{3} \log _{3} y-5 \log _{3} w-\frac{1}{2} \log _{3} z \) C. \( { }^{2} \log _{3} x+3 \log _{3} y-5 \log _{3} w-2 \log _{3} z \) D. This cannot be simplified.

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.

b. \( -0.5 p+\frac{1}{2} p-2.75+\frac{2}{3} \)