Evaluate \( -\frac{4}{5} x z \) if \( x=-\frac{2}{3} \) and \( z=-1 \frac{7}{8} \). Write in simplest form

To evaluate \( -\frac{4}{5} x z \) with \( x = -\frac{2}{3} \) and \( z = -1 \frac{7}{8} \), we first convert \( z \) into an improper fraction. The mixed number \(-1 \frac{7}{8}\) can be converted as follows: \[ -1 \frac{7}{8} = -\left(1 + \frac{7}{8}\right) = -\left(\frac{8}{8} + \frac{7}{8}\right) = -\frac{15}{8} \] Now we substitute \( x \) and \( z \) into the expression: \[ -\frac{4}{5} x z = -\frac{4}{5} \left(-\frac{2}{3}\right) \left(-\frac{15}{8}\right) \] First, let's calculate \( -\frac{4}{5} \left(-\frac{2}{3}\right) \): \[ =-\frac{4}{5} \cdot -\frac{2}{3} = \frac{4 \cdot 2}{5 \cdot 3} = \frac{8}{15} \] Now we multiply this result by \(-\frac{15}{8}\): \[ \frac{8}{15} \cdot -\frac{15}{8} = -\frac{8 \cdot 15}{15 \cdot 8} \] Since both 8 and 15 in the numerator and denominator cancel out: \[ = -1 \] Thus, the final answer in simplest form is: \[ \boxed{-1} \]