There is no fundamental way to value money. Money is in a permanent state of bubble, and there is no fundamental way to value something in a bubble.
Therefore, there is no fundamental way to value an exchange rate. All you have are historical prices. The only reason the health of a country's economy affects the price of its national currency is because people expect it to, but it doesn't have to.
Imagine a government issues a new currency: one million blank pieces of green paper. These will find a market value. If the same government issues another currency, one million blank pieces of blue paper, these will also find a market price. They are effectively different currencies. Just because they are issued by the same government, and the same quantity, there is no reason why they should reach the same price. People might start using one for small change, and one for higher-value transactions.
Imagine instead that the government issues green and blue paper as above, but prints the number "10" on the greens and "1" on the blues. Now we might expect them to trade at a ratio of precisely 10 to 1, and they are effectively one currency.