\(\dfrac{2^{18}\cdot18^7\cdot3^3+3^{15}\cdot2^{15}}{2^{10}\cdot6^{15}+3^{14}\cdot15\cdot4^{13}}\)
\(=\dfrac{2^{18}\cdot\left(2\cdot3^2\right)^7\cdot3^3+2^{15}\cdot3^{15}}{2^{10}\cdot\left(2\cdot3\right)^{15}+3^{14}\cdot\left(3\cdot5\right)\cdot\left(2^2\right)^{13}}\)
\(=\dfrac{2^{18}\cdot2^7\cdot3^{14}\cdot3^3+2^{15}\cdot3^{15}}{2^{10}\cdot2^{15}\cdot3^{15}+3^{15}\cdot2^{26}\cdot5}\)
\(=\dfrac{2^{25}\cdot3^{17}+2^{15}\cdot3^{15}}{2^{25}\cdot3^{15}+2^{26}\cdot3^{15}\cdot5}\)
\(=\dfrac{2^{15}\cdot3^{15}\left(2^{10}\cdot3^2+1\right)}{2^{25}\cdot3^{15}\left(1+2\cdot5\right)}\)
\(=\dfrac{2^{10}\cdot3^2+1}{2^{10}\cdot11}\)
\(=\dfrac{9217}{11264}\)
#Toru
\(=\dfrac{2^{18}\cdot2^7\cdot3^{14}\cdot3^3+3^{15}\cdot2^{15}}{2^{10}\cdot2^{15}\cdot3^{15}+3^{15}\cdot5\cdot2^{26}}\)
\(=\dfrac{2^{15}\cdot3^{15}\left(2^{10}\cdot3^2+1\right)}{2^{25}\cdot3^{15}\left(1+5\cdot2\right)}=\dfrac{2^{10}\cdot3^2+1}{2^{10}\cdot11}\)
