\(\dfrac{81^4\cdot3^{10}\cdot27^5:3^{12}}{3^{18}:9^3\cdot243^2}=\dfrac{\left(3^4\right)^4\cdot3^{10}\cdot\left(3^3\right)^5:3^{12}}{3^{18}:\left(3^2\right)^3\cdot\left(3^5\right)^2}\)

\(=\dfrac{3^{16}\cdot3^{10}\cdot3^{15}:3^{12}}{3^{18}:3^6\cdot3^{10}}=\dfrac{3^{16+10+15-12}}{3^{18-6+10}}=\dfrac{3^{29}}{3^{22}}=3^7=2187\)

814⋅310⋅275:312318:93⋅2432=(34)4⋅310⋅(33)5:312318:(32)3⋅(35)2

=316⋅310⋅315:312318:36⋅310=316+10+15−12318−6+10=329322=37=2187