\(\dfrac{75.5^4+175.5^4}{20.25.125-625.75}\)
\(=\dfrac{5^4\left(175+75\right)}{4.5.5^2.5^3-5^4.5^2.3}=\dfrac{5^4.225}{4.5^6-3.5^6}\)
\(=\dfrac{5^4.225}{4.5^6-3.5^6}=\dfrac{5^4.15^2}{5^6\left(4-3\right)}=\dfrac{5^4.\left(5.3\right)^2}{5^6}=\dfrac{5^4.5^2.3^2}{5^6}=\dfrac{5^6.3^2}{5^6}=9\)