Question

(3.4.2^16)^2/11.2^13.4^11-16^9

Answer 1

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

\(=\dfrac{3^2.\left(2^2\right)^2.\left(2^{16}\right)^2}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\) 

\(=\dfrac{3^2.2^4.2^{32}}{11.2^{13}.2^{22}-2^{36}}\) 

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

\(=\dfrac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\) 

\(=\dfrac{3^2.2^{36}}{2^{35}.9}\) 

\(=\dfrac{3^2.2^{36}}{2^{35}.3^2}\) 

\(=2\)

Answer 2

(3.4.2^16)^2/11.2^13.4^11−16^9=3^2.(2^2)^2.(2^16)^2/11.2^13.(2^2)^11−(2^4)^9=3^2.2^4.2^32/11.2^13.2^22−2^36=3^2.2^36/11.2^35−2.2^35=3^2.2^36/2^35.(11−2)=3^2.2^36/2^35.9=3^2.2^36/2^35.3^2=2