Question

Answer 1

\(\dfrac{16^3\cdot3^{10}+120\cdot6^9}{4^6\cdot3^{12}+6^{12}}\)

\(=\dfrac{2^{12}\cdot3^{10}+2^3\cdot3\cdot5\cdot2^9\cdot3^9}{2^{12}\cdot3^{12}+2^{12}\cdot3^{12}}\)

\(=\dfrac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{13}\cdot3^{12}}=\dfrac{1}{2}\cdot\dfrac{1}{9}\cdot6=\dfrac{1}{2}\cdot\dfrac{2}{3}=\dfrac{1}{3}\)

Answer 2

\(\dfrac{2^{12}.3^{10}+2^3.5.2^9.3^9}{2^{12}.3^{12}+2^{12}.3^{12}}\)

\(\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{13}.3^{12}}\)

\(\dfrac{2^{13}.3^{11}.}{2^{13}.3^{12}}\)

\(\dfrac{1}{3}\)