The statement that best investigates why the Spanish and Portuguese were able to influence Indigenous communities in Latin America is:
The destruction caused by widespread disease allowed Europeans to more effectively change weakened Indigenous culture.
This statement acknowledges the significant impact that diseases brought by Europeans had on Indigenous populations, which often led to demographic collapse and weakened social structures. This vulnerability made it easier for Spanish and Portuguese colonizers to exert influence and impose their cultures and systems of governance. While the other statements contain elements of truth, they do not capture the crucial role of disease in the dynamics of cultural influence.