Why were Cuba, Haiti, and the Dominican Republic vital to emerging American power in the Carribean?

Cuba, Haiti, and the Dominican Republic were vital to emerging American power in the Caribbean because:

In the Caribbean, the countries of Cuba, Haiti, and the Dominican Republic were very important in the quest for America to consolidate their power base.

This was because they  were previous occupied by Spain and France, and by this new found territories, America's power base grew stronger as they were taking on more territories around the world.

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Cuba, Haiti and the Dominican Republic were very important for the emerging American power in the Caribbean because they were territories formerly in the possession of the European powers (Spain and France), which once independent limited the power of these nations in the region.

Thus, the fact that Cuba, Haiti and the Dominican Republic were constituted as independent nations caused the European colonial powers to lose weight in the Caribbean Sea, leaving a power vacuum that was used by the United States to establish itself as the main power of the region.

"a problem throughout latin america is widespread poverty. what can those countries improve? the higher the literacy rate" or "education, the lower the rate of poverty".

although the majority of the total population and the population   poor in latin america and the caribbean is in the centers   urban areas, in relative terms poverty remains a   rural phenomenon in the region. the incidence of poverty and   extreme poverty is much greater in rural areas than   in urban areas without going further, in 1997 more than half of the   rural households lived in poverty and about a third in   situation of extreme poverty. in addition, the difficult economic situation   of most of the countries in the region in the past   two years has surely deteriorated those figures. to the poor   of the rural areas of the region are raised at least   three basic problems: i); insufficient nutrition, poor health and   poor educational services; ii); scarce opportunities   productive employment in agriculture and non-agricultural activities;   and iii); low degree of organization to effectively promote   the rural interests. the number and variety of circumstances   that cause rural poverty, as well as heterogeneity   of conditions in which it occurs in different countries   and regions hinder the search for effective solutions and   efficient to raise the welfare of the rural population.  

the mechanisms to reduce poverty are   focuses on three types of important action possibilities and   complementary to generate or raise the income of the poor   of rural areas: one that is based on the growth of   agricultural sector; another that aims at sustainable use and conservation   of natural resources, and the last based on the importance   growing rural economic activities that   they develop outside the agricultural land. there are at least other   two possibilities for reducing rural poverty: the traditional migration to urban areas and assistance to   people who need income transfers to overcome   the poverty threshold or to have a minimum access to   social safety nets.

it created the power of judicial review.