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.

Solution
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