Like any other good, money’s exchange value or price is determined by its total stock and the total demand people have to hold the stock. Each fiat currency of the world has a price or purchasing power within the area in which it is legal tender money and a price or exchange rate against each of the other currencies in the world. Exchange rates adjust to keep the purchasing power of any one currency, say the dollar, the same everywhere. So with the demand for all the currencies held constant, if the Fed inflates the stock of dollars to a certain extent and every other country inflated its currency to the same extent, then every country would experience price inflation domestically and yet the exchange rates between currencies would be stable. If the Fed massively inflated dollars, then we would have hyperinflation domestically. If other countries only modestly inflated their currencies, the our hyperinflation would be associated with dollar devaluation against other currencies. If other countries massively inflated their currencies, then our hyperinflation would not have dollar devaluation against other currencies.
What has been moderating our price inflation in the face of Fed monetary expansion is an offsetting increase the demand to hold dollars. The monetary policy of other countries cannot affect the purchasing power of the dollar unless it affects the demand to hold dollars. Lacking this, monetary policy of other countries will affect exchange rates, but not the purchasing power of the dollar. Faster inflation of a foreign currency relative to the dollar will result in an appreciating dollar relative to the foreign exchange and vice versa for slower inflation of a foreign currency relative to the dollar.