The correct spelling for the phrase "study at element" is: /'stʌdi æt 'ɛlɪmənt/. The word "study" is spelled with the letters "s-t-u-d-y" and pronounced /'stʌdi/. "At" is spelled as "a-t" and is pronounced /æt/. Lastly, "element" is spelled with the letters "e-l-e-m-e-n-t" and pronounced as /'ɛlɪmənt/. The IPA phonetic transcription system is used to explain the pronunciation of words in English. It helps learners to understand how to pronounce words correctly and improves their overall communication ability.