It took ten (1998-2008) years before the US minimum wage went up.
That's 10 years without a pay rise for the unskilled worker of America.
It that's not an example of worker exploitation I don't know what is?
Additionally, in your example while the federal minimum wage might not have increased many states have their own minimum wage laws that have changed over the period you describe.
The closest statement you could make is that an absence of minimum wage laws may make it legal to employ people at an exploitatively low wage. This is not really the name thing.
To answer this question you have to go no further than to study history.
When there where no minimum wage laws workers where exploited.
You have to go back no further than the first industrial revolution to see evidence of this.
Now that exploitation brought about the rise of the union movement.
I don't think it is a coincide that as we now witness the decline of the union movement, there is a corresponding rise in the exploitation of workers.
Those who don't study their history are destined to repeat it.