What regions of the world had europeans explored by the late 1700s
how did early european voyage of discovery opens up new trade routes to the new world

The Americas!  The discovery of the new world opened up a new output for products like gold and silver.  (Especially silver for Spain)  The Columbian exchange resulted in foods such as the potato being brought over to Europe.  Did you know the first potatoes were actually from Peru!  Labor animals like cows and bulls were brought over to the new world. This was basically the only good thing about the Columbian exchange for the AMericas.  Europe mostly just gave the Americas disease and death.

Why do you have to ask such hard questions.

Because the discoveries were some of the oldest human remains.