The spelling of the word "CASE SOAP III" can be explained through the use of IPA phonetic transcription. The first sound in the word is represented by the 'k' consonant sound, followed by the 'eɪ' diphthong sound as in 'ray'. The 's' sound is represented by the IPA symbol /s/, while the 'oʊ' diphthong sound as in 'go' follows. The next sound is 'p', represented by the /p/ symbol. The word also includes the Roman numeral 'III', which indicates the third iteration of the product.