Question

 B=\(\dfrac{6^{12}.200-2^{15}.5^2.180}{6^{11}.60-2^{14}.450}\)

Answer 1

\(=\dfrac{2^{12}\cdot2^3\cdot3^{12}\cdot5^2-2^{15}\cdot5^2\cdot2^2\cdot3^2\cdot5}{2^{11}\cdot3^{11}\cdot2\cdot3\cdot5-2^{14}\cdot2\cdot3^2\cdot5^2}\)

\(=\dfrac{2^{15}\cdot3^{12}\cdot5^2-2^{17}\cdot5^3\cdot3^2}{2^{12}\cdot3^{12}\cdot5-2^{15}\cdot3^2\cdot5^2}\)

\(=\dfrac{2^{15}\cdot3^2\cdot5^2\left(1-2^2\cdot5\right)}{2^{12}\cdot3^2\cdot5\left(3^{10}-2^3\cdot5\right)}=\dfrac{2^3\cdot5\cdot\left(1-20\right)}{3^{10}-40}\)

\(=\dfrac{-760}{59009}\)