This should be correct for at least 50 digits after decimal point:

 
1141973130130727445029596475.97165373568561208619839490929389898529956
+04918087368059784750017004880305063884032742217053556637130
[download]

calculated using Math::BigFloat (which operates decimal with configurable precision) and taking advantage of exponentiation laws described here.

(NB: BigFloat's own ->bpow() method is far slower)

use strict;
use warnings;
use Math::BigFloat;

my $exp=6e7;
Math::BigFloat->precision(-100);
my $x=Math::BigFloat->new('1.000001');
my $val=Math::BigFloat->new('1');
$\="\n";


for my $bit (reverse split //,sprintf '%b',$exp) {
    # print "$bit ",$x;
    $val->bmul($x) if $bit;
    $x->bpow(2);
}

$val->bmul(10);

print "Result : $val";

my $syphilis=Math::BigFloat->new('1141973130130727445029596475.971760'
+);

print "diff: ", $val - $syphilis;
[download]

took about a second on a netbook.

Compilation started at Tue Jan 20 02:19:30

/usr/bin/perl -w /home/lanx/pm/big_expo.pl 
Result : 1141973130130727445029596475.97165373568561208619839490929389
+89852995604918087368059784750017004880305063884032742217053556637130
diff: -0.0001062643143879138016050907061010147004395081912631940215249
+982995119694936115967257782946443362870

Compilation finished at Tue Jan 20 02:19:31
[download]

The results from the C-libs are as you can see only accurate till the third digit after decimal point.

I'm not a big expert on BigFloat, if you see a problem, all feedback welcome. :)

update

you can easily increase the accuracy to 1000 digits after decimal point by setting precision to -1050, only takes a second.