Question

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

Answer 1

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

Answer 2

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

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

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

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

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

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

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

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

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