Polyatomic Ions

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How to name ionic compounds that contain polyatomic ions. How to name and write formulas of oxo anions and oxo acids.
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Is there some way to figure out how they got the formula/charges for the ones in the table? Like phosphate has PO4^-3 as its formula but oxygens charge is -6 and phosphorous is -5. Where did the four and the negative three come from? My professor expects us to get the formula for phosphate from the information on the periodic table and naming conventions.

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