British | A nice Exponential problem | Math Olympiad

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[@ivansouza6468]

(9/4)^9^4
(3^2/2^2)^9/4
[(3/2)^2]^9/4. 2.9/4 = 9/2
(3/2)^9/2
√3^9/√2^9
81√3/16√2
81√3.√2 = 81√6
16√2.√2 = 16.2 = 32
81√6/32

[@nikolayguzman331]

More faster: (9/4)^(9/4) = (9/4)^(2+ 1/4); (9/4)^(2+1/4) = (9/4)^2 * (9/4)^(1/4); (81/16) * ((3/2)^2)^(1/4)=(81/16) * (3/2)^(1/2).