\(\dfrac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
\(=\dfrac{3^2.\left(2^2\right)^2.\left(2^{16}\right)^2}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\)
\(=\dfrac{3^2.2^4.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)
\(=\dfrac{3^2.2^{36}}{11.2^{35}-2.2^{35}}\)
\(=\dfrac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\)
\(=\dfrac{3^2.2^{36}}{2^{35}.9}\)
\(=\dfrac{3^2.2^{36}}{2^{35}.3^2}\)
\(=2\)
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