a: \(=\dfrac{5^5\cdot4^5\cdot5^{10}}{\left(5^2\right)^5\cdot4^5}=\dfrac{5^{15}}{5^{10}}=5^5\)
b: \(=\dfrac{\left(0.3\right)^{10}}{\left(0.3\right)^6}=\left(0.3\right)^4\)
c: \(=\dfrac{3^3\cdot2^3+3^3\cdot2^2+3^3}{-13}=\dfrac{3^3\cdot13}{-13}=-27\)
d: \(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot5}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{4}{5}\)