Simplify: \( -\left(\frac{2 c^{4}}{3 d^{5}}\right)^{-3} \)

To simplify \( -\left(\frac{2 c^{4}}{3 d^{5}}\right)^{-3} \), we start by addressing the negative exponent. Using the rule \( a^{-n} = \frac{1}{a^n} \), we can rewrite the expression: \[ -\left(\frac{2 c^{4}}{3 d^{5}}\right)^{-3} = -\frac{1}{\left(\frac{2 c^{4}}{3 d^{5}}\right)^{3}} \] Next, we simplify the denominator: \[ \left(\frac{2 c^{4}}{3 d^{5}}\right)^{3} = \frac{(2)^{3} (c^{4})^{3}}{(3)^{3} (d^{5})^{3}} = \frac{8 c^{12}}{27 d^{15}} \] Now substituting this back into our expression, we have: \[ -\frac{1}{\frac{8 c^{12}}{27 d^{15}}} \] To take the reciprocal of the fraction, we rewrite it as: \[ -\frac{27 d^{15}}{8 c^{12}} \] Finally, we conclude with the simplified expression: \[ -\frac{27 d^{15}}{8 c^{12}} \]