How do I evaluate the expression? (729/216)^2/3 (144/25)^3/2?

(144/25)^(3/2) = [(144/25)^(1/2)]^3

The (1/2) power is just a square root, so that's:

= (12/5)^3

The same idea works on the first factor, only with cube roots:

(729/216)^(2/3) = [(729/216)^(1/3)]^2 = (9/6)^2 = (3/2)^2

So:
(729/216)^(2/3) (144/25)^(3/2) = (3/2)^2 (12/5)^3
= (3^2 12^3) / (2^2 5^3) ... but 2^2 on the bottom cancels with one 12 on top
= (3^3 12^2) / 5^3 ... making an extra factor of 3 on top
= 3888 / 125

Presentation is incorrect and should be :-

[ 729 / 216 ]^(2/3) [ 144 / 25 ]^(3/2)

[ 81 / 36 ] [ 1728 / 125 ]

[ 9 / 4 ] [ 1728 / 125 ]

9 x 432 / 125

3888 / 125 = 31•104