  In 1958, Sierpinski asked whether there exists a linear order $X$ that is
isomorphic to its lexicographically ordered cube but is not isomorphic to its
square. The main result of this paper is that the answer is negative. More
generally, if $X$ is isomorphic to any one of its finite powers $X^n$, $n>1$,
it is isomorphic to all of them.
