Solving a 'Harvard' University entrance exam question

[00:00:00]Hello Friends (9/4)^(9/4)=?

[00:00:05]let's have a solution so, we have a problem of (9/4)^(9/4) 9 is same as 3^2 and 4 is same as 2^2 (3^2/2^2)^(9/4) It can be written as {(3/2)^2}(9/4) (3/2)^(2.9/4) where 2.2=4 we have (3/2)^(9/2) (3/2)^((4+4+1)/2) where 9 is same as (4+4+1) separate it into fractions, (3/2)^(4/2+4/2+1/2) 2.2=4 (3/2)^(2+2+1/2) (3/2)^(4+1/2) as we know a^(m+n)=a^m.a^n then It will be (3/2)^4.(3/2)^(1/2) next (3^4/2^4).√(3/2) 3^4=3.3.3.3=81 and 2^4=2.2.2.2=16 then It will be 81/16.√3/√2 this is same as 81√3/16√2.(√2/√2) next, we have 81√(3.2)/16√(2.2) 81√6/16√4 so we have 81√6/16.2 where √4=2 finally, we get our answer (9/4)^(9/4)=81√6/32 which is our final answer thanks for watching this video please subscribe this channel to get the notification of my new videos and don't forget to share this video with your classmates and friends so that they also have a benefit of it ok bye