The correct spelling of the phrase "study at booty" is actually "study abroad." This phrase means to study at a university or educational institution outside of one's home country. The reason for the mistake in spelling is likely due to a mishearing of the phrase. In IPA phonetic transcription, "study abroad" is represented as /ˈstʌdi əˈbrɔːd/, while "study at booty" would be transcribed as something like /ˈstʌdi æt ˈbuːti/. It's important to pay close attention to pronunciation and context in order to avoid spelling errors like this one.