\(\text{a},10^8.2^8=\left(10.2\right)^8=20^8\\ b,10^8:2^8=\left(10:2\right)^8=5^8\\ c,25^4.2^8=25^4.\left(2^2\right)^4=\left(25.2^2\right)^4=100^4\\ d,15^8.9^4=15^8.\left(3^2\right)^4=15^8.3^8=\left(15.3\right)^8=45^8\\ e,27^2:25^3=\left(3^3\right)^2:\left(5^2\right)^3=3^6:5^6=\left(3:5\right)^6=\left(\dfrac{3}{5}\right)^6\)