And most of the time, a for/push combination converts very naturally to a map:

my @sets;
for my $x (1..3){
  my @products = map { $x ** $_ } (1..3);
  push @sets, \@products;
}
use Data::Dumper;
print Dumper(\@sets);
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Then we still have a for/push. Since we have to use $_ for our loop variable in map, it might seem a little tricky, but we're nesting these, so we can do this:

my @sets = map {
  my $x = $_; # Copy outer loop variable
  my @products = map { $x ** $_ } (1..3);
  \@products;
} (1..3);
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Of course, there's no real need for the @products array:

my @sets = map {
  my $x = $_; # Copy outer loop variable
  [map { $x ** $_ } (1..3)];
} (1..3);
[download]