Why are C++ Exponents rounding?

I have some very simple C++ code:

#include "stdafx.h"
#include "math.h"

int main(int argc, char* argv[])
{
    long double i,t,c;
    i = 16;
    t = 27;
    c = powl(i, t);

    printf ("%f",  c ); 
    printf ("\n");
    return 0;
}

According to Microsoft's calculation in Windows, 16^27 is:

3.2451855365842672678315602057626e+32

According to C++ it is:

324518553658426730000000000000000.000000

Why is this difference in precision happening? It must be completely precise, I am trying to make something simple that will encrypt a message in RSA"

Cipher text = Message **_^ E_** Mod N

If the exponent isn't computed precisely, it will come out incorrect.

Is there anything else that I could define that would be completely precise and hold that large of a number? If someone could direct me towards a class that would do precise math such as this it would be greatly appreciated.