If r, s, and t are constants such that\( \frac{x^{r-2}\cdot y^{2s}\cdot z^{3t+1}}{x^{2r}\cdot y^{s-4}\cdot z^{2t-3}}=xyz\) for all non-zero x, y, and z, then solve for \(r^s\cdot t\). Express your answer as a fraction.

Hint: substitute 1 for y and 1 for z to find r, then substitute 1 for x and 1 for z to find s, and then substitute 1 for x and 1 for y to find t.