No it is not like that
As usa prices rise by 10-5=5% more than Europe's, usa exports fall because they are now more expensive and usa imports from Europe rise since they are now relatively less costly. Thus there is more demand for euros and less demand for dollars. This depreciates dollars. Now usa prices are greater by 5%. On the other hand in terms of euros the prices of dollars fall by 5% due to depreciation of dollars. So for European customers 5-5=0.so in this sense relative purchasing power remains same.
Note depreciation means dollars can now buy less and in terms of euros they are now cheaper. Exchange rate means no. Of dollars required to buy a euro and depreciation here means this no. rises. It will not increase price level of dollar. Dollars price is euros which falls.
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