Let \[x_2=\{n\ | 1\leq n\leq 200, n=k^2\ \exists k\in \z\},\] \[x_3=\{n\ | \ 1\leq n\leq 200, n=k^3\ \exists k\in \z\},\] and \[x_4 = \{n\ | \ 1\leq n\leq 200, n=k^4\ \exists k\in \z\}.\] determine $|x_2\cup x_3\cup x_4|$.