 Concatenation \(uv\) of words \(u, v\) is associative because when a word is cut into two, the concatenation of the two parts is the original word regardless of where the cut is made. The concatenation of al and gebra is the same as that of algeb and ra, illustrating associativity of concatenation for the case \(x = \) al, \(y =\) geb, \(z =\) ra.