The answer to your stated problem is (approximately): 

1.62675140326585151695359576572305028615189801780017874401138747953366
+6153159557
7231689168104895638321577104465527647015203626362603998098979186946926
+8832653563
9876783696445088873548169461692031716658344408349608575969073401085646
+9974613384
9405956337321357208524215023135129502713155156225709454163291397424581
+6205784347
5431740808707270038873430922419306290943341499184229388612632870411538
+6624697621
1861673434551121694807279905899572891343788110628871316393375609771228
+8741592371
0603410526214509643406584397169902292984256457451844313620574254135229
+8152022680
9667066503022068942686945186662371921322607350580802347649425019123435
+6116588173
3499576581595447507264764340471182267254547886431989042026739164206635
+2222527744
3185422437032044145067492037856780857407031186997008368115810653126418
+5732353764
8593952946070043338085483314164347241434879451637334242547144110143792
+0986573147
31499871814441453762083542077883230646... × 10^3834649

[download]

As you can see, for full accuracy, however you calculate it, it's gonna take a while. So, rather than eschewing the use of approximations, you're going to have to decide how much accuracy you actually need?

Also, it's often the case for calculations that generate these silly numbers, that they are only intermediate terms, with the final results being numbers much more in the realms of reality. And often, it is possible (and very desirable) to avoid the silly-sized intermediate terms by cancelling like terms earlier in the calculation. Describing your actual purpose may lead to better solutions.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
RIP an inspiration; A true Folk's Guy

In reply to Re: how to multiply an array of number as fast as posible by BrowserUk
in thread how to multiply an array of number as fast as posible by baxy77bax

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • 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, details, 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, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.