Just use a (generally considered evil) string eval in both cases:

...

print '$z is: ', $z, "\n";
print 'eval of $z is: ', eval $z, "\n";
print 'eval of "2 * 3" is: ', eval '2 * 3', "\n";
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Prints:

$z is: 2 * 3
eval of $z is: 6
eval of "2 * 3" is: 6
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