\(\left(\frac{9}{16}\right)^{2016}.\left(\frac{16}{9}\right)^{2015}.\frac{4}{3}\)
\(=\left(\frac{9}{16}\right)^{2015}.\left(\frac{16}{9}\right)^{2015}.\frac{9}{16}.\frac{4}{3}\)
\(=\left(\frac{9}{16}.\frac{16}{9}\right)^{2015}.\frac{3}{4}\)
\(=\frac{1.3}{4}=\frac{3}{4}\)