25. \( \frac{-6 a^{3} b^{10} c}{12 a^{8} b^{4} c} \)

To simplify the expression \( \frac{-6 a^{3} b^{10} c}{12 a^{8} b^{4} c} \), start by simplifying the coefficients and canceling out like terms. The coefficient \(-6\) divided by \(12\) gives \(-\frac{1}{2}\). For the \(a\) terms, \(a^{3}\) in the numerator and \(a^{8}\) in the denominator simplifies to \(a^{-5}\) or \(\frac{1}{a^{5}}\). The \(b\) terms simplify as \(b^{10}\) divided by \(b^{4}\) equals \(b^{6}\). The \(c\) terms cancel each other out since they are the same. Putting it all together, the simplified expression is \(-\frac{1}{2} \times \frac{b^{6}}{a^{5}}\), or \(-\frac{b^{6}}{2a^{5}}\).