\(\frac{\left(3\cdot2^{18}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}\)
\(=\frac{3^2+2^{18\cdot2}}{11\cdot2^{13}\cdot4^{11}-16^9}\)
\(=\frac{3^2\cdot2^{36}}{11\cdot2^{13}\cdot\left(2^2\right)^{11}-\left(2^4\right)^9}\)
\(=\frac{3^2\cdot2^{36}}{11\cdot2^{13}\cdot2^{22}-2^{36}}\)
\(=\frac{3^2\cdot2^{36}}{11\cdot2^{35}-2^{36}}\)
\(=\frac{3^2\cdot2^{36}}{11\cdot2^{35}-2^{35}\cdot2}\)
\(=\frac{9\cdot2^{35}\cdot2}{2^{35}\left(11-2\right)}\)
\(=\frac{9\cdot2^{35}\cdot2}{2^{35}\cdot9}\)
\(=\frac{2}{1}=2\)
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