Using the in-built capabilities of your language, calculate the integer value of:

        
  
    
      
        
          5
          
            
              4
              
                
                  3
                  
                    2
                  
                
              
            
          
        
      
    
    {\displaystyle 5^{4^{3^{2}}}}
  


 Confirm that the first and last twenty digits of the answer are: 
     62060698786608744707...92256259918212890625

 Find and show the number of decimal digits in the answer.


Note: Do not submit an implementation of arbitrary precision arithmetic. The intention is to show the capabilities of the language as supplied. If a language has a single, overwhelming, library of varied modules that is endorsed by its home site – such as CPAN for Perl or Boost for C++ – then that may be used instead.
Strictly speaking, this should not be solved by fixed-precision numeric libraries where the precision has to be manually set to a large value; although if this is the only recourse then it may be used with a note explaining that the precision must be set manually to a large enough value.


Related tasks

   Long multiplication
   Exponentiation order
   exponentiation operator
   Exponentiation with infix operators in (or operating on) the base


#include <iostream>
#include <boost/multiprecision/gmp.hpp>
#include <string>
 
namespace mp = boost::multiprecision;
 
int main(int argc, char const *argv[])
{
    // We could just use (1 << 18) instead of tmpres, but let's point out one
    // pecularity with gmp and hence boost::multiprecision: they won't accept
    // a second mpz_int with pow(). Therefore, if we stick to multiprecision
    // pow we need to convert_to<uint64_t>().
    uint64_t tmpres = mp::pow(mp::mpz_int(4)
                            , mp::pow(mp::mpz_int(3)
                                    , 2).convert_to<uint64_t>()
                                      ).convert_to<uint64_t>();
    mp::mpz_int res = mp::pow(mp::mpz_int(5), tmpres);
    std::string s = res.str();
    std::cout << s.substr(0, 20) 
              << "..."
              << s.substr(s.length() - 20, 20) << std::endl;
    return 0;
}
 