Express the following fraction in simplest form, only using posit \[ \frac{3 q^{2}}{-2\left(p^{3} q^{-5}\right)^{-1}} \]

To simplify the fraction \[ \frac{3 q^{2}}{-2\left(p^{3} q^{-5}\right)^{-1}}, \] we first simplify the denominator. According to the properties of exponents, the expression \(\left(p^{3} q^{-5}\right)^{-1}\) can be rewritten as follows: \[ \left(p^{3} q^{-5}\right)^{-1} = p^{-3} q^{5}. \] Now substituting this back into the denominator gives: \[ -2\left(p^{3} q^{-5}\right)^{-1} = -2(p^{-3} q^{5}) = -2p^{-3} q^{5}. \] Now the entire expression becomes: \[ \frac{3q^{2}}{-2p^{-3}q^{5}}. \] To simplify it further, we can rewrite it as: \[ \frac{3q^{2}}{-2} \cdot \frac{1}{p^{-3}q^{5}}. \] This can be rewritten as: \[ \frac{3q^{2}}{-2} \cdot \frac{p^{3}}{q^{5}} = \frac{3p^{3}q^{2}}{-2q^{5}}. \] Now, we simplify the \(q\) terms: \[ \frac{3p^{3}}{-2q^{3}}. \] So, the simplified form of the given fraction is \[ \frac{-3p^{3}}{2q^{3}}. \]