0) \( \frac{-12 a^{4} b c^{5}}{+3 a^{3} b^{3} c} \)

To simplify the expression: \[ \frac{-12 a^{4} b c^{5}}{+3 a^{3} b^{3} c} \] Follow these steps: 1. **Simplify the Coefficients:** \[ \frac{-12}{3} = -4 \] 2. **Simplify the Variables by Subtracting Exponents:** - For \( a \): \[ \frac{a^{4}}{a^{3}} = a^{4-3} = a^{1} = a \] - For \( b \): \[ \frac{b}{b^{3}} = b^{1-3} = b^{-2} = \frac{1}{b^{2}} \] - For \( c \): \[ \frac{c^{5}}{c} = c^{5-1} = c^{4} \] 3. **Combine the Simplified Parts:** \[ -4 \times a \times c^{4} \times \frac{1}{b^{2}} = \frac{-4 a c^{4}}{b^{2}} \] **Final Simplified Expression:** \[ \boxed{\dfrac{-4 a\, c^{4}}{\,b^{2}\,}} \]