If you have log available, you can use Newton method to easyly find the solution to the equation f(z) = log(z)  y * log x = 0 :
#!/usr/bin/perl
use strict;
use warnings;
my ($X, $Y, $n) = @ARGV;
$n = 20;
my $Z = $X ** $Y;
# f(z) = log z  y * log x = 0;
# f'(z) = f1(z) = 1/z
my $ylogx = $Y * log $X;
my $z = 1;
for my $i (1..$n) {
my $fz = log($z)  $ylogx;
my $f1z = 1 / $z;
$z = $z  $fz / $f1z;
my $e = abs($z  $Z);
printf "%3d: z=%8f, e=%8f\n", $i, $z, $e;
}
This method does not handle correctly values of y < 0 but this is not a problem because z(y) = 1 / z(y).
Also, note that even if the algorithm converges in very few iterations, it uses log that is usually an expensive operation and so, other methods requiring more iterations may be actually faster.
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
 a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
Outside of code tags, you may need to use entities for some characters:

For: 

Use: 
 &   & 
 <   < 
 >   > 
 [   [ 
 ]   ] 
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.

