Exclusive jurisdiction is when only a single court, or a type of court, has jurisdiction over the matter in question. An easy example for this is that the United States District Courts have exclusive jurisdiction in cases of bankruptcy, or that the Supreme Court has exclusive jurisdiction on reviewing other courts' decisions.
Some key motives for Europeans during the Age of Exploration was they wanted to find a new sea route to Asia, they wanted knowledge, they wanted to spread Christianity, they wanted wealth and glory, and they wanted spices.
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