\(\frac{5^{10}.\left(7^3-7^4\right)}{\left(125.7\right)^3+\left(125.7.2\right)^3}=\frac{5^{10}.7^3.\left(1-7\right)}{125^3.7^3+125^3.7^3.2^3}\)
\(=\frac{5^{10}.7^3\left(-6\right)}{125^3.7^3.\left(1+2^3\right)}=\frac{5^{10}.7^3.\left(-6\right)}{\left(5^3\right)^3.7^3.\left(1+8\right)}\)
\(=\frac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}=\frac{-10}{3}\)