executive branch
State supreme courts (or their equivalent) are part of each State's Judicial branch.
The government does not belong to a branch, it has branches. The government is divided into three branches: the legislative, executive, and judicial. They all have different functions in terms of the law.
legislative
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lawmakers are elected
judical
the executive is the correct answer
President Obama is in the Executive Branch of the government. (Congress is the Legislative Branch, and the Supreme Court is called the Judicial Branch.)
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The governor belongs to the executive branch of state government.
judicial