Step 1: Hydrolysis of P\(_4\)O\(_{10}\).
When phosphorus pentoxide (P\(_4\)O\(_{10}\)) reacts with water, it hydrolyzes to form phosphoric acid (H\(_3\)PO\(_4\)):
\[
P_4O_{10} + 6 H_2O \rightarrow 4 H_3PO_4
\]
Step 2: Heating above 320°C.
When phosphoric acid (H\(_3\)PO\(_4\)) is heated above 320°C, it undergoes dehydration to form polyphosphoric acids, which are a mixture of HPO\(_3\) and (HPO\(_3\))\(_n\) (i.e., chains of phosphoric acid molecules):
\[
n H_3PO_4 \rightarrow (HPO_3)_n + (n-1) H_2O
\]
Step 3: Conclusion.
The correct compounds formed are H\(_3\)PO\(_4\) upon hydrolysis and (HPO\(_3\))\(_n\) upon heating above 320°C.
Final Answer:
\[
\boxed{H_3PO_4 \text{ and } (HPO_3)_n}
\]