Which is correct?

British powerful army
Or
British's powerful army
I think the first one is right.

Neither. Use any of these:

... powerful British army
... Britain's powerful army
... the powerful army of Britain

Thank you!

You are correct. The first sentence, "British powerful army," is correct. When describing a noun with an adjective, the possessive form (using an apostrophe) is not necessary. In this case, "British" is used as an adjective to describe the type of army, and there is no possession involved. Therefore, the proper way to describe it is "British powerful army."