ta có :(9/16)^2016.(16/9)^2015.4/3=9^2016/16^2016.16^2015/9^2015.4/3

=9^2016.16^2015.4/16^2016.9^2015.3=1/2

bạn viết ra giấy cho dễ nhìn nhá

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

= \(\frac{9}{16}\) . \(\frac{4}{3}\) = \(\frac{36}{48}\) = \(\frac{3}{4}\)

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

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

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

\(=\frac{1.3}{4}=\frac{3}{4}\)

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

                                                     \(=\frac{9}{16}.\frac{4}{3}\)

                                                         \(=\frac{3}{4}\)

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

                                                 \(=\frac{9}{16}\cdot\frac{4}{3}\)

                                                 \(=\frac{3}{4}\)

\(=\frac{9}{16}.\frac{4}{3}\)

\(=\frac{3}{4}\)

=\(\frac{3}{4}\)

= 3/8

(calculator  đúng)

\(\frac{3}{4}\)

3653/224

\(\left(\dfrac{9}{16}\right)^{2016}.\left(\dfrac{16}{9}\right)^{2015}.\dfrac{4}{3}\)

\(=\left[\left(\dfrac{3}{4}\right)^2\right]^{2016}.\left[\left(\dfrac{4}{3}\right)^2\right]^{2015}.\dfrac{4}{3}\)

\(=\left(\dfrac{3}{4}\right)^{2018}.\left(\dfrac{4}{3}\right)^{2017}.\dfrac{4}{3}\)

\(=\left(\dfrac{3}{4}\right)^{2018}.\left(\dfrac{4}{3}\right)^{2018}\)

\(=\left(\dfrac{3}{4}.\dfrac{4}{3}\right)^{2018}\)

\(=\left(\dfrac{1}{1}.\dfrac{1}{1}\right)^{2018}\)

\(=1^{2018}\)

\(=1\)