using the identity (a+b)(a-b)=a^2-b^2

mutlitply and divide the given question by (2-1)..
{(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)}/(2-1)=
(2^2-1)(2^2+1)(2^4+1)(2^8+1)=
(2^4-1)(2^4+1)(2^8+1)=
(2^8-1)(2^8+1)=
2^16-1