$bigNumber = Math::BigInt->new(6) ** Math::BigInt->new(25);
Or simply:
$bigNumber = Math::BigInt->new(6) ** 25;
Perl will print 6 ** 25 as 2.84302880299297e+019 and doing Math::BigInt->new(6 ** 25) therefore becomes Math::BigInt->new(2.84302880299297e+019), which Math::BigInt interprets literally as Math::BigInt->new(28430288029929700000). And that's how AlligatorStamp gets the value he observed.
With perl, we can also see the actual value by doing:
C:\>perl -le "printf '%0.f', 6 ** 25;"
28430288029929701376
And the same should work with AlligatorStamp's perl-5.14.2 ... unless he's running ActivePerl, in which case it will be 28430288029929701000.
Cheers,
Rob
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