[tex] \left(2^8\cdot \:3^{-5}\cdot \:1\right)^{-2}=\left(1\cdot \frac{256}{243}\right)^{-2}=\left(\frac{256}{243}\right)^{-2}=\left(\frac{243}{256}\right)^2 [/tex]
[tex] \left(2^8\cdot \:3^{-5}\cdot \:6^0\right)^{-2}\left(\frac{3^{-2}}{2^3}\right)^4\cdot \:2^{28} [/tex]
[tex] =2^{28}\left(\frac{3^{-2}}{2^3}\right)^4\left(3^{-5}\cdot \:2^8\cdot \:1\right)^{-2} [/tex]
Consider
[tex] \left(2^8\cdot \:3^{-5}\cdot \:1\right)^{-2}=\left(1\cdot \frac{256}{243}\right)^{-2}=\left(\frac{243}{256}\right)^2=\frac{243^2}{256^2} [/tex]
[tex] =2^{28}\left(\frac{3^{-2}}{2^3}\right)^4\frac{243^2}{256^2} [/tex]
[tex] =2^{28}\cdot \frac{1}{2^{12}\cdot \:3^8}\cdot \frac{243^2}{256^2} [/tex]
[tex] =\frac{243^2\cdot \:1\cdot \:2^{28}}{256^2\cdot \:3^8\cdot \:2^{12}} [/tex]
[tex] =\frac{2^{16}\cdot \:243^2}{3^8\cdot \:256^2} [/tex]
[tex] =\frac{2^{16}\cdot \:3^{10}}{2^{16}\cdot \:3^8} [/tex]
[tex] =3^2 [/tex]
[tex] =9 [/tex]
