An ablative absolute is a phrase made up of a NOUN and a PARTICIPLE in the ablative case. Therefore they both need ablative endings. Use this formula to translate an ablative absolute with a perfect participle:With X having been Y e.g. deo laudato - with the god having been praised The participle needs to agree with the noun in CASE, GENDER, and NUMBER. 'deo' is a masculine singular ablative noun. Therefore the masculine singular ablative ending is needed for the participle.Perfect participle endings are always in the 1st or 2nd declension depending on their gender. a - for feminine singularo - for masculine/neuter singularis - for all pluralsNote that perfect participles can still only have this endings even when a 3rd declension noun is used. e.g. urbe capta - with the city having been captured 'Urbe' is a feminine singular ablative 3rd declension noun. Therefore, the feminine singular ablative ending 'a' is required for the participle capta.These are trickier to spot so make sure you always look out for the ablative endings even when they aren't the same.