Well, because this looks really like a homework question I give you the following hint:

What is PSAPCE exactly? How is "time" measured in sense of a turing computation?
With these prerequesites, why is any problem, which is in PSPACE, "by definition" in EXPTIME?

Hope, I could give you some sketch

Edit (more hints): Okay, you have to be a bit more precise with your definitions: PSPACE is a set whereby, for all $A \in PSPACE$ there exists a Turing-Machine $M$, that can compute on an input $x$ with length $n$, if $x$ is a solution of the problem $A$ with at most using polynomial space on the turing working tape: 
Formal: Let $x_0 ... x_i$ denote the cells of $M$, which are used (that means, the read/write head of $M$ visits this cell at least once) during the computation.