Proof

In the following scheme you find all the different ways to view the expression 

x1 * x2 * x3 * x4

as a result of three times applying the operation * together with the equalities obtained by a direct application of the associativity law. 

((x1 * x2) * x3) * x4 =
(x1 * x2) * (x3 * x4) =
x1 * (x2 * (x3 * x4)) =
x1 * ((x2 * x3) * x4) =
(x1 * (x2 * x3)) * x4

In general one can show by induction on the number n of variables that an expression can be transformed into 

( ··· (x1 * x2) * x3) * ··· xn).

The details of this proof are left to the reader.