14) \( \frac{3 x^{6} y^{8} z^{5}}{2 x^{8} y^{5} z^{7} \cdot-8 z x^{-4} \cdot-4 x y^{0} z^{0}} \)

First, let's simplify the expression step by step. We start with the given expression: \[ \frac{3 x^{6} y^{8} z^{5}}{2 x^{8} y^{5} z^{7} \cdot -8 z x^{-4} \cdot -4 x y^{0} z^{0}} \] First, we can simplify the denominator: 1. The product of the constants in the denominator: \(2 \cdot -8 \cdot -4 = 64\). 2. The variable parts of the denominator: - \(z\) has \(z^{7} \cdot z^{1} \cdot z^{0} = z^{8}\). - \(x\) has \(x^{8} \cdot x^{-4} \cdot x^{1} = x^{5}\) (noting that \(y^{0} = 1\)). - \(y\) has \(y^{5} \cdot y^{0} = y^{5}\). So, the complete denominator becomes: \[ 64 x^{5} y^{5} z^{8} \] Now, substituting back into the fraction we have: \[ \frac{3 x^{6} y^{8} z^{5}}{64 x^{5} y^{5} z^{8}} \] Now we can cancel out variables in the fraction: For \(x\): \[ x^{6} \div x^{5} = x^{1} = x \] For \(y\): \[ y^{8} \div y^{5} = y^{3} \] For \(z\): \[ z^{5} \div z^{8} = z^{-3} = \frac{1}{z^{3}} \] Putting this all together, we get: \[ \frac{3 x y^{3}}{64 z^{3}} \] Hence, the final simplified expression is: \[ \frac{3 x y^{3}}{64 z^{3}} \]