In order to ease away some difficulty (like an exam), is it ok to fast for it?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Generally speaking, doing good deeds increases Taqwa (piety) and Eeman (Faith), and fasting is included within good deeds.

Allah Says about the righteous (what means): {And whosoever fears Allah and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine.} [Quran 65: 2-3]
Allah also Says (what means): {…and whosoever fears Allah and keeps his duty to Him, He will make his matter easy for him.} [Quran 65: 4]

Just as doing good deeds makes a way for one to get out from difficulty, doing misdeeds constitutes a reason to be befallen by difficulties and distress.

Allah also Says (what means): {And whoever turns away from My remembrance - indeed, he will have a depressed life, and We will gather him on the Day of Resurrection blind."} [Quran 20: 124]

In the same vein, the Prophet said: “A human being is deprived of livelihood due to committing a sin." [Ahmad]

Based on the above, we state that there is no objection to observe fasting with the intention you specified in your question (i.e., to have an easy exam).

Therefore, we advise you to avoid misdeeds and sins at the same time, since committing sins opens the door of evil.

Allah knows best.