Question

how was the national assembly recognised n how did it start exercising its power​

Answer 1

therefore your answer is verified there

Answer 2

Faced with revolting people, Louis XVI recognised the national assembly and accepted that his powers would from now on checked by the constitution.

National assembly started exercising its power in the following ways :—

1. On the night of 4th August, 1789, the assembly passed the law for abolishing feudal system of obligation and taxes, the clergy members were also forced to give up their privileges.
2. Tithes were abolished and lands owned by the church were seized and all this resulted in acquiring assets what at least two billion livres.