\(B=\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)
\(B=\dfrac{2\cdot\left(2^3\right)^4\cdot\left(3^3\right)^2+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^2\cdot10\cdot\left(3^2\right)^4}\)
\(B=\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^{14}\cdot3^7+2^9\cdot10\cdot3^8}\)
\(B=\dfrac{2^{11}\cdot2^2\cdot3^6+2^{11}\cdot3^6\cdot3^3}{2^{11}\cdot2^3\cdot3^6\cdot3+\dfrac{2^{11}}{2^2}\cdot10\cdot3^6\cdot3^2}\)
\(B=\dfrac{\left(2^{11}\cdot3^6\right)\left(2^2+3^3\right)}{\left(2^{11}\cdot3^6\right)\left(2^3\cdot3\right)+2^{11}\cdot\dfrac{1}{2^2}\cdot10\cdot3^6\cdot3^2}\)
\(B=\dfrac{\left(2^{11}\cdot3^6\right)\left(2^2+3^3\right)}{\left(2^{11}\cdot3^6\right)\left(2^3\cdot3+\dfrac{1}{2^2}\cdot10\cdot3^2\right)}\)
\(B=\dfrac{2^2+3^3}{2^3\cdot3+\dfrac{1}{2^2}\cdot10\cdot3^2}\)
\(B=\dfrac{4+27}{8\cdot3+\dfrac{1}{4}\cdot10\cdot9}\)
\(B=\dfrac{31}{24+\dfrac{1}{4}\cdot90}\)
\(B=\dfrac{31}{24+\dfrac{45}{2}}\)
\(B=\dfrac{31}{\dfrac{48}{2}+\dfrac{45}{2}}\)
\(B=\dfrac{31}{\dfrac{93}{2}}\)
\(B=31\div\dfrac{93}{2}\)
\(B=31\times\dfrac{2}{93}\)
\(B=\dfrac{2}{3}\)
