aura ete AND auraient ete English translations

Question

In the lesson above, the translation is given as "will have been" and "would have been" respectively.  How do I distinguish between them in choosing the right translation?  Thank you

Accepted Answer

They are 2 different French tenses : 'aura été' is future anterior (singular, 3rd person), and 'auraient été' (plural 3rd person) is past conditional. 
('auront éte' for 3rd person plural future anterior; aurait été for 3rd person singular past conditional)
In English, 'would'  is ambiguous without context, as it can be either conditional or past tense, but in French the verb expressions are distinct. 
The 2 links below cover the features of these 2 tenses in French:
https://progress.lawlessfrench.com/revision/glossary/conjugation-tense-mood-aspect/french-future-perfect-tense-le-futur-anterieur-indicatif
https://progress.lawlessfrench.com/revision/glossary/conjugation-tense-mood-aspect/french-conditional-past-tense-le-conditionnel-passe