It can also be mathematically shows that in order to export more goods and services than we import, we would have to devalue the US dollar. The easiest way to see this is to look at the relation between the Capital Account and the Current Account. The Current Account is the net export of goods and services. The Capital Account is the net export of assets. It's is always the case that,
Current Account + Capital Account = 0.
When you buy an imported good, you must pay for it with something (realizing here that the dollar itself is an asset). For every import of a good or service, there is a corresponding export, even if that export is an asset rather than another good or service. If you want to export more goods than you import, then you must import more assets than you export. Since our biggest asset of export is the dollar itself, a rise in the export of goods means a fall in the export of dollars. Said another way, foreigners wouldn't want to hold dollars. Surely we can see that a loss of the reserve status of the dollar, or a weaker dollar, should be approached with caution.
Another way to see how a rise in exports means a fall in the dollar is to look at GDP accounting.
PQ = Y = C + I + G + (X-M)
P = Price level
Q = Quantity of output
Y = Total output
C = consumption
I = Investment
G = gov't spending
X = Exports of goods
M = imports of goods
The Law of One Price states that the price of a good in one country should be the same as that of the price of that same good in another country. So, an apple in the US priced in US dollars should be the same price as an apple in Canada priced in Canadian dollars multiplied by the exchange rate. So the price level of US goods in US dollars is equal to the price level of goods in some foreign currency multiplied by the exchange rate,
P[usd] = S*P[xxx]; where S = usd/xxx and xxx = some foreign currency
we can see then that,
S*P[xxx]*Q = C + I + G + (X - M)
And now we can look at what happens when the values of imports and exports of goods changes in the economy. For ease of analysis, let's hold C, I, and G constant for the moment. And let's say that there is a huge trade deficit so that imports (M) are much greater than exports (X). Then a policy change is made to ensure that exports grow relative to imports. As net exports (X-M) approach 0, it must be the case that such a change is met by a fall in the price level of the foreign country (P[xxx]), a fall in production of the USA (Q), and/or a strengthening of the foreign currency relative to the US currency (S = usd/xxx).
The initial response would most likely be a fall in the dollar relative to the foreign currency as firms exploited the opportunity for profit by selling their goods at the higher foreign price in the foreign country in the foreign country's currency. As more goods flooded the foreign market, the price level would fall.
Over the long run, the equilibrium would tend toward the law of one price,
P[usd] = S*P[xxx]
Take away:
A rise in exports of goods means a fall in exports of highly traded domestic assets. The chief of these highly traded domestic assets is the dollar itself. So a rise in exports means a fall in the dollar's value in addition to a rise in price of goods that were formerly imported from country xxx.
The only way this wouldn't be the case is if either consumption growth, domestic investment growth, and/or government spending growth outpaced the growth of exports.