\(\left(\dfrac{3}{2}\right)^7:\left(\dfrac{7}{2}\right)^5+\dfrac{3}{2}\)
\(=\left(\dfrac{3}{2}\right)^5:\left(\dfrac{7}{2}\right)^5\cdot\dfrac{9}{4}+\dfrac{3}{2}\)
\(=\left(\dfrac{3}{2}:\dfrac{7}{2}\right)^5\cdot\dfrac{9}{4}+\dfrac{3}{2}\)
\(=\left(\dfrac{3}{7}\right)^5\cdot\dfrac{9}{4}+\dfrac{3}{2}\)
\(=\dfrac{2187}{67228}+\dfrac{3}{2}=\dfrac{103029}{67228}\)