(6^3*4^2-8^2*27^2):(6^4*2^2-9^3*4^2)

=(6³*4²-8²*27²)/((6²)²*2²-9³*4²)= [latex]= \frac{( 2^{3} * 3^{3} * 2^{4} - 2^{6} * 3^{6} )}{( 2^{4} * 3^{4} * 2^{2} - 3^{6} * 2^{4} )} =[/latex] [latex]= \frac{ 2^{6} * 3^{3} * ( 2 - 3^{3} )}{2^{4} * 3^{4} * ( 2^{2} - 3^{2} )} = [/latex] [latex]= \frac{ 2^{2} * ( 2 - 3^{3} )}{ 3 ( 2^{2} - 3^{2} )} [/latex] =4*(2-27)/(3*(4-9))=4*(-25)/(3*(-5))=-100/(-15)= 6,(6)