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

sai r bn ơi

-_-

không hiểu

(9/16)^2016.(16/9)^2015.4/3

9/16.(9/16)^2015.(16/9)^2015.4/3

9/16.(9/16.16/9)^2015.4/3

9/16.1^2015.4/3

9/16.1.4/3

=>9/16.4/3=3/4

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

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

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

k cho mk nhoa

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

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

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

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

\(=\frac{9}{16}.1^{2015}.\frac{4}{3}\)

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

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

\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{9999}{10000}\)

\(=\frac{1\cdot3}{2^2}\cdot\frac{2\cdot4}{3^2}\cdot\frac{3\cdot5}{4^2}\cdot...\cdot\frac{99\cdot101}{100^2}\)

\(=\frac{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)...\left(99\cdot101\right)}{2^2\cdot3^2\cdot4^2\cdot...\cdot100^2}\)

\(=\frac{\left(1\cdot2\cdot3\cdot...\cdot99\right)\left(3\cdot4\cdot5\cdot101\right)}{\left(2\cdot3\cdot4\cdot...\cdot100\right)\left(2\cdot3\cdot4\cdot...\cdot100\right)}\)

\(=2\cdot101=202\)

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

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

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

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

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

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

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

= 3/8

(calculator  đúng)