use strict;
use warnings;

my $x = <STDIN>;
$x *= 1;
print "String\n" if ($x =~ /\w/);
print "Integer\n" if ($x =~ /\d/);
print $x**$x ."\n";

__OUTPUT__
e
Argument "e\n" isn't numeric in multiplication (*) at tmp.pl line 8, <
+STDIN> line 1.
String
Integer
1
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Now consider the following code (use lines removed for brevity):

my $x = <STDIN>;
print "String\n" if ($x =~ /\w/);
print "Integer\n" if ($x =~ /\d/);
print $x**$x ."\n";

__OUTPUT__
e
String
Argument "e\n" isn't numeric in exponentiation (**) at tmp.pl line 13,
+ <STDIN> line 1.
1
[download]

Lastly, consider this piece of code forcing the string or integer into integer context. Notice the exponentiation doesn't throw an error because the input was forced into integer context.

my $x = <STDIN>;
$x *= 1;
print "String\n" if ($x =~ /\w/);
print "Integer\n" if ($x =~ /\d/);
print $x**$x ."\n";
__OUTPUT__
2
String
Integer
4
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Note: The reason its a string and an integer is in the case of \w (which is what the regex uses), it checks for [0-9a-zA-Z] as well.