What are the factors that underlie currency exchange values in a free market?This is an International economics question.

Currency exchange values or exchange rates refer to the
price of one national currency in term of some other national currency. For example;
presently one US$ can be exchanged in the international markets for about 45 Indian
rupees.

The exchange rate are determined primarily by the
relative demand for different currency. This in turn is reflected by the purchasing
powers of the currency as well as government. If there is a greater demand for Japanese
goods in the US then this will tend to push up the price of Japanese yen in terms of
US$. A system that allows the exchange rates of currency of a country to be determined
completely by the market forces is called floating exchange rate. However many countries
do try to regulate the exchange rates of their currency and put some restriction on
their free movement.

Countries may keep their currency rate
stable by backing their currency by some standards item of value such as gold. For
example for a long time the US$ was committed to redeem its currency at the rate of one
ounce of Gold for 35$. However most of the countries have now abandoned the system of
gold standards. Since 1970's most countries follow the floating rate system in which
price of a currency rises or falls in relation to other countries is response to their
demand in the international markets. However in practice, governments do intervene by
selling or buying their own currency if there is steep rise or fall in exchange rates
that is considered counter to the interest of the
country.

Since the early 1970's, the major trading
countries have had floating exchange rates.  With such rates, the price of a nation's
currency rises and falls in relation to world demand for that currency.  This demand in
turn is influenced heavily by the imports and exports of a country and the prices at
which various goods are being sold and purchased by the country. Exchange rates of the
currency of a country is likely to rise when id sell goods cheap in comparison to other
countries and when its exports exceed its imports.

However,
most governments intervene if the exchange rate for their currency rises or falls too
far and take steps to prevent an excessive change.  For this reason, the system is often
called managed floating.