A goal of the African union is to

establish peaceful diplomatic relationships amongst all African countries.
provide dictatorship-style forms of government across Africa.
establish a political division in African countries that operate out of self-interest.
support the ethnic cleansing efforts of corrupt rebel groups.

The African Union's goal is to establish peaceful diplomatic relationships amongst all African countries. This includes promoting cooperation, democracy, and good governance in order to prevent conflicts and maintain stability in the region. It does not support dictatorship-style governments, political divisions driven by self-interest, or ethnic cleansing efforts by corrupt rebel groups. The African Union focuses on promoting unity, human rights, and development across the continent.

The goal of the African Union is to establish peaceful diplomatic relationships amongst all African countries.

The correct answer is: "establish peaceful diplomatic relationships amongst all African countries."

To arrive at this answer, we first need to understand what the African Union is and its goals. The African Union (AU) is a continental organization that consists of 55 member states in Africa. Its primary goal is to promote unity, cooperation, and development amongst African countries.

Next, we eliminate the incorrect answer choices:

- "Provide dictatorship-style forms of government across Africa" is incorrect because the AU's goal is to promote democracy, good governance, and respect for human rights. The AU encourages member states to uphold democratic principles and practices.

- "Establish a political division in African countries that operate out of self-interest" is also incorrect. The AU works towards building unity and encouraging member states to work together for the common good of Africa, rather than promoting self-interest or divisions.

- "Support the ethnic cleansing efforts of corrupt rebel groups" is a completely incorrect statement. The AU strongly opposes any form of violence, ethnic cleansing, or activities that harm the welfare of African people. It aims to promote peace, security, and stability.

Hence, the correct answer is that the goal of the African Union is to "establish peaceful diplomatic relationships amongst all African countries."