$power=Math::BigInt->new($initial_index);
$distance_index=($power->bpow($distance))->numify();

##</code><code>##

cmpthese -3, {
    BigInt => q[
        my $x = Math::BigInt->new( $_ )->bpow( 4 )->numify() for 2 .. 1e6; 
    ],
    standard => q[ 
        my $x =  $_ ** 4 for 2 .. 1e6;
    ],
};;
            (warning: too few iterations for a reliable count)

         s/iter   BigInt standard
BigInt      172       --    -100%
standard  0.625   27472%       --