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.

First, let's substitute \( x = 5 \), \( y = -9 \), and \( z = 5 \) into the expression: \[ \left(\frac{1}{6} \cdot 5 - \frac{1}{4} \cdot (-9)\right)\left(-\frac{8}{9} \cdot 5\right) \] Calculating \( \frac{1}{6} \cdot 5 = \frac{5}{6} \) and \( -\frac{1}{4} \cdot (-9) = \frac{9}{4} \). To combine those, we need a common denominator, which is 12: \[ \frac{5}{6} = \frac{10}{12}, \quad \frac{9}{4} = \frac{27}{12} \] Now, \[ \frac{10}{12} + \frac{27}{12} = \frac{37}{12} \] Next, calculate \( -\frac{8}{9} \cdot 5 = -\frac{40}{9} \). Now, we have \[ \left(\frac{37}{12}\right)\left(-\frac{40}{9}\right) \] Multiply these fractions: \[ = -\frac{37 \cdot 40}{12 \cdot 9} = -\frac{1480}{108} \] Now, simplify the fraction \( -\frac{1480}{108} \): \[ = -\frac{370}{27} \quad \text{(after dividing both numerator and denominator by 4)} \] Thus, the answer is: A. \( \left(\frac{1}{6} x-\frac{1}{4} y\right)\left(-\frac{8}{9} z\right) = -\frac{370}{27} \)