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

To evaluate \( -\frac{3}{5} x z \) with \( x = -\frac{1}{3} \) and \( z = -1 \frac{5}{8} \), we first convert \( z \) into an improper fraction. The mixed number \( -1 \frac{5}{8} \) can be converted as follows: \[ -1 \frac{5}{8} = -\left(1 + \frac{5}{8}\right) = -\left(\frac{8}{8} + \frac{5}{8}\right) = -\frac{13}{8} \] Now we can substitute \( x \) and \( z \) into the expression: \[ -\frac{3}{5} x z = -\frac{3}{5} \left(-\frac{1}{3}\right) \left(-\frac{13}{8}\right) \] Multiplying the fractions together, we have: \[ -\frac{3}{5} \cdot -\frac{1}{3} \cdot -\frac{13}{8} \] This simplifies to: \[ -\frac{3 \cdot 1 \cdot 13}{5 \cdot 3 \cdot 8} \] Here, the \( -\frac{3}{3} \) will cancel: \[ -\frac{13}{5 \cdot 8} = -\frac{13}{40} \] Thus, the expression evaluates to: \[ -\frac{13}{40} \] Since we are looking for the simplest form, and \( 13 \) is a prime number (it has no common factors with \( 40 \)), the simplest form of the result is: \[ -\frac{13}{40} \]