Is it possible?

$c$ is a positive integer , then , also $c^2$ is positive integer ,

Let's write the equation again : $a^4+b^4=(c^2)^4$ , where $a,b,c^2$ are three positive integers ,

According to Fermat's last theorem , no three positive integers $r,s,t$ satisfy the equation $r^n+s^n=t^n$ , for any interger value for $n$ greater than $2$ ,

If $r=a,s=b,t=c^2,n=4$ we can see that the answer is "No".