= 3^2 . 2^4 . 2^32 / 11.2^13 .2^22 - 2^36

=3^2 . 2^36 / 11.2^35 - 2^36

=3^2 . 2^36 / 2^35 . ( 11+2)

= 9 . 2^36 / 2^35 . 13 

= 9 . 2 / 13 = 18/13

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

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

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

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

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

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

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

\(=2\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(=2\)

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