Evaluate the expression if \( x=5, y=-9 \), and \( z=5 \). \( \left(\frac{1}{6} x-\frac{1}{4} y\right)\left(-\frac{8}{9} z\right) \) Select the correct choice below and fill in any answer boxes within your choice. A. \( \left(\frac{1}{6} x-\frac{1}{4} y\right)\left(-\frac{8}{9} z\right)=\square \) (Type an integer or a simplified fraction.) B. The answer is undefined.

We start with the expression \[ \left(\frac{1}{6}x - \frac{1}{4}y\right)\left(-\frac{8}{9}z\right) \] and substitute \( x = 5 \), \( y = -9 \), and \( z = 5 \). 1. Evaluate the first part: \[ \frac{1}{6}x - \frac{1}{4}y = \frac{1}{6}(5) - \frac{1}{4}(-9) \] This becomes \[ \frac{5}{6} + \frac{9}{4} \] 2. Find a common denominator to add the fractions. The least common denominator of 6 and 4 is 12: \[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}, \quad \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \] Now add them: \[ \frac{10}{12} + \frac{27}{12} = \frac{37}{12} \] 3. Evaluate the second part: \[ -\frac{8}{9}z = -\frac{8}{9}(5) = -\frac{40}{9} \] 4. Multiply the two results: \[ \frac{37}{12} \times \left(-\frac{40}{9}\right) = -\frac{37 \times 40}{12 \times 9} = -\frac{1480}{108} \] 5. Simplify the fraction by dividing the numerator and denominator by 4: \[ \frac{1480 \div 4}{108 \div 4} = \frac{370}{27} \] The negative sign remains: \[ -\frac{370}{27} \] Thus, the evaluated expression is \[ -\frac{370}{27} \] A. \(\left(\frac{1}{6} x-\frac{1}{4} y\right)\left(-\frac{8}{9} z\right)=-\frac{370}{27}\)