Perfect Powers Square

In the following 2x2 grid,

8 4
1 6

there are 6 different perfect powers: 1, 4, 8, 16, 64, 81.
  1. Fill a 3x3 grid with single digits to get the largest number of perfect powers. Numbers are read up, down, left or right (not diagonally), and are 1, 2 or 3 digits long.
  2. Repeat #1 with the restriction that all nine digits be unique.

Source: Original.

Solutions were received from Philippe Fonanaiche: 
Excluding the numbers read diagonally (this is not the case of your example),I
have got the following squares:
832
169
144 with 14 different perfect powers:1,4,8,9,16,32,36,49,64,81,144,169,441,961

or
729
836
441 with also 14 perfect powers:1,4,8,9,16,27,32,36,144,169,441,729,784,961

With the restriction of the 9 digits being unique,I have got:
725
834
169 with 13 perfect powers 1,4,8,9,16,25,27,32,36,49,81,169,961

Denis Borris : 

Using the diagonals:
137
625
948   (17 Powers: 1 4 8 9 16 25 27 32 36 49 64 128 169 324 625 729 961)
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