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

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\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

\(=\frac{3^2.2^{36}}{11.2^{34}-2^{36}}\)

\(=\frac{3^2.2^{36}}{2^{34}.\left(11-2^2\right)}\)

\(=\frac{9.2^{36}}{2^{34}.7}\)

\(=\frac{36}{7}\)

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

\(=\frac{3^2.4^2.2^{32}}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\)

\(=\frac{9.\left(2^2\right)^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)

\(=\frac{9.2^4.2^{32}}{11.2^{35}-2^{36}}\)

\(=\frac{9.2^{36}}{2^{35}.\left(11-2\right)}\)

\(=\frac{9.2^{35}.2}{2^{35}.9}\)

\(=2\)

\(=\frac{3^2\cdot2^{36}}{11\cdot2^{35}-2^{36}}=\frac{3^2\cdot2^{36}}{2^{35}\left(11-2\right)}=\frac{3^2\cdot2}{9}=2\)

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

= \(=\frac{\left(3.2^2.2^{16}\right)^2}{11.2^{13}.\left(2^2\right)^{11}-\left(24\right)^9}\)

\(=\frac{\left(3.2^{18}\right)^2}{11.2^{13}.2^{22}-2^{36}}\)

\(=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}\)

\(=\frac{9.2^{35}.2^1}{11.2^{35}-2^{36}}\)

\(=\frac{18.2^{35}}{11.2^{35}-2^{36}}\)

\(=\frac{18.2^{35}}{11.2^{35}-2^{35}.2^1}\)

\(=\frac{18.2^{35}}{\left(11-2\right).2^{35}}\)

\(=\frac{18.2^{35}}{9.2^{35}}=2\)

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}=2\)

\(=\frac{3^2.4^2.2^{32}}{11.2^{35}-2^{36}}\)

\(=\frac{3^2.4^2.2^{32}}{2^{35}\left(11-2\right)}\)

\(=\frac{3^2.4^2.2^{32}}{2^{35}.3^2}\)

\(=\frac{4^2}{2^3}\)

\(=\frac{2^4}{2^3}\)

\(=2\)

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