I see you haven't read perlfunc yet.

print ( 2**3 - 1 )**( 2**7 - 1 ) % ( 2**19 - 1 )
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is equivalent to

( print ( 2**3 - 1 ) )**( 2**7 - 1 ) % ( 2**19 - 1 )
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and not the

print( ( 2**3 - 1 )**( 2**7 - 1 ) % ( 2**19 - 1 ) )
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that you think it is.

That's why I put a + before the first parenthesis - it's one of the few times where a unary + is highly significant.

UPDATE: added the word "unary"