Question

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

Answer 1

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

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

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

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

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

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

\(=1^{2018}\)

\(=1\)