Lets say I got to prove that $(X_1\times X_2 \times X_3\times \cdots X_{n-1})\times X_n$ is homeomorphic to $(X_1\times X_2 \times X_3\times \cdots X_n)$
I just define the function as
$f((x_1,x_2,\cdots x_{n-1}),x_n)=(x_1,x_2\cdots x_n)$ .... THen I can prove it right @anon