`Answer:`
\(A=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}.\frac{63}{64}\)
\(=\frac{8.15.24.35.48.63}{9.16.25.36.49.64}\)
\(=\frac{2^3.3.5.2^3.3.5.7.2^4.3.3^2.7}{3^2.2^4.5^2.2^2.3^2.7^2.2^6}\)
\(=\frac{3}{2^2}\)
\(=\frac{3}{4}\)