Final answer:
The European penetration into the Asian trading system by 1600 was primarily facilitated by the influx of silver from mines in Peru and Mexico, enabling them to trade effectively with silver-seeking Asian markets.
Step-by-step explanation:
The success of the European powers in penetrating the Asian trading system by 1600 can best be explained by the opening of rich silver mines in Peru and Mexico. This influx of silver allowed the Europeans to trade for Chinese goods, given that China had moved to silver as their monetary base. Europe's economic structures were heavily based on gold and silver, a source of significant fortune for Spain, which facilitated trade and allowed European powers to establish lucrative trade routes to Asia. The Portuguese and the Spanish were first to navigate these waters, soon followed by the English.