\(a,4^3.8^2.27^4=\left(2^2\right)^3.\left(2^3\right)^2.\left(3^3\right)^4=2^6.2^6.3^{12}=2^{12}.3^{12}=\left(2.3\right)^{12}=6^{12}\\ b,27^4.81^2.16^5=\left(3^3\right)^4.\left(3^4\right)^2.\left(2^4\right)^5=3^{12}.3^8.2^{20}=3^{20}.2^{20}=\left(3.2\right)^{20}=6^{20}\\ c,5^3.25^4.125^2=5^3.\left(5^2\right)^4.\left(5^3\right)^2=5^3.5^8.5^6=5^{3+8+6}=5^{17}\\ d,10^2.100^3.1000000^3=10^2.\left(10^2\right)^3.\left(10^6\right)^3=10^2.10^6.10^{18}=10^{2+6+18}=10^{26}\)