In a study of harmonic resonances, a physicist models the fundamental dampening constant D D\,D as the term independent of ω \omega\,ω in the binomial expansion of P(ω)=(32ω2−4ω3)10P(\omega) = \left( \dfrac{3}{2}\omega^2 - \dfrac{4}{\omega^3} \right)^{10}P(ω)=(23ω2−ω34)10. Calculate the exact value of DDD.
