Cabozantinib and Androgen Ablation in Patients With Androgen-Dependent Metastatic Prostate Cancer

Study Drug Administration: If you are found to be eligible to take part in this study, you will take 1 capsule of cabozantinib by mouth 1 time every day while you are on study. You should not eat or drink anything other than water for 2 hours before and 1 hour after taking the study drug. You should take the capsule with at least 1 cup (8 ounces) of water. You will also be given separate directions about how to take the study drug. You will also receive hormone therapy. The hormone drug you receive will be standard of care hormone therapy. The study doctor will decide what hormone therapy you will receive and will explain when and how you should take the hormone therapy, as well as its risks. You will be given a drug diary where you will record when you take cabozantinib. You should return this diary to the study staff when you come into the clinic. Study Visits: At every visit, you will be asked about any side effects you may have had and any other drugs you may be taking. If you are receiving Coumadin, every week for the first 3 weeks, you will have blood drawn (about 1 teaspoon) to test your blood clotting function. Every 3 weeks for the first 12 weeks of the study, and then every 6 weeks after that: * You will have a physical exam. * Blood (about 3-4 teaspoons) will be drawn for routine tests. Every 3 weeks for the first 12 weeks of the study, and then every 12 weeks after that, blood (about 1 teaspoon) will be drawn to check your thyroid and pancreatic function. The frequency of the testing may change if the study doctor thinks it is needed. Every 6 weeks, you will have the following tests performed: * Blood (about 2-3 teaspoons) will be drawn to measure your PSA levels and for biomarker testing. * Urine will be collected for routine tests. * You may have these test performed near your home if the study doctor thinks you are tolerating the treatment. Every 12 weeks, you will have a bone scan and CT scans of the chest, abdomen, and pelvis to check the status of the disease. Length of Study: You may continue receiving the study drug for as long as the study doctor thinks it is in your best interest. You will be taken off study early if the disease gets worse, if you have intolerable side effects, or if your study doctor thinks it is in your best interest to stop. Long-Term Follow-Up: You will be contacted every 6 months after you stop taking the study drug to check on how you are feeling and the status of the disease. This will consist of a phone call, e-mail, or medical record review. If you are called, each call should last about 5 minutes. This is an investigational study. Cabozantinib is FDA approved to treat patients with certain types of thyroid cancer. Its use in this study is investigational. Up to 60 participants will take part in this study. All will be enrolled at MD Anderson.