"She said that each time she took the test, she had trouble in particular with the standardized, multiple-choice portion of the exam. After her fourth failure, she and a friend who also struggled with it went to Portland, Ore., to take a preparatory course. During the course, they learned strategies for successfully tackling the standardized portion. Murkowski returned to Alaska and passed the bar exam. She was so impressed with the company that offered the prep course, PMBR, that for several years afterward she was its representative in Alaska." Sounds like she finally passed because she learned some test-taking strategies, not because she learned more about the law. I'll give her points for persistence (obviously, since she's currently engaged in a Quixotesque write-in campaign). This is hardly evidence that she might be a better Senator than the Republican candidate who is a Yale Law School graduate and was awarded a Bronze Star.
She waited until the fourth failure before taking a bar prep course? Yikes, she isn't stupid, she is a fool! Law schools don't teach you the law in a particular state, they teach you the concepts and the different sides to an issue, with some exceptions (model codes, Federal laws, etc...).
Each state is different, some more so than others. For instance, Louisiana state law is based on the Napoleonic code and VA is based on the common law, so the same situation could come out very different depending upon which state it occurred in.
I spent three years of my life and many thousands of dollars to go to a law school, so spending a few thousand dollars and three months learning VA law was a "no brainer."