Question

\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^3.3\right)^6+8^4.3^5}=?\)

Answer 1

\(\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^3\cdot3\right)^6+8^4\cdot3^5}=\frac{2}{579}\)

Answer 2

\(=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{18}\cdot3^6+2^{12}\cdot3^5}=\frac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^5\left(2^6\cdot3+1\right)}=\frac{2^{12}\cdot3^4\cdot2}{2^{12}\cdot3^5\cdot193}=\frac{2}{3\cdot193}=\frac{2}{579}\)