Just as price is a function of supply and demand, so are exchange rates. The money supply is independent of the price of goods and of the price of currencies (exchange rates).

Seemingly, a larger overall quantity of dollars in existence would seem to predict a decline in the value of the dollar relative to other currencies, but the monetary policy decisions that resulted in increased money supply are intended to achieve relative price stability.

For example, the dollars introduced to the economy and lent to banks had the effect of encouraging banks to make loans, which helped increase demand for products and services, which helped prevent prices from falling.

Also, many of the dollars are being used as reserve capital after the market price of various securities which had been used as reserve capital declined, leaving the entities under-capitalized. All this was done in an attempt to keep interest rates low (in effect a price target) and prevent banks from being forced to stop lending money...

So I think the bottom line is that the behavior of consumers and firms can account for so much variability in supply and demand that the money supply can expand greatly and prices can still say roughly constant... the other side of the coin being that monetary policy was used to keep prices relatively stable, in this case by keeping the credit infrastructure status quo alive.

edit: Of course, if the Fed gets it wrong or lacks the will to raise interest rates when necessary, hyperinflation can result, which would impact exchange rates.