The use of exhaust, thanks

No. You could say
I am exhausted and sweating/sweaty.
I am exhausted and soaked/bathed in sweat.

Thank you very much Mentor Ble Jay,
for you kind advices.
How about
I am so exhausted that I was bathed in sweat.
Can this sound fine to you?

Not really. Logically, you can be exhausted without being sweaty, and you can be sweaty without being exhausted.
As far as the structure of the sentence is concerned, you should stick to the same verb tense in the sentence, am....am or was....was.
I am so exhausted that I am unable to climb the stairs to my bedroom.
I was so exhausted th

Thank you so much.
I am taking exhaustion as the result of hard work (cleaning the house!), so the result of hard work would be both exhaustion and sweat. Isn't that logical?
regards

Yes, but being exhausted and being sweaty would be two separate consequences of your hard work. You would be sweaty because you had been working hard, not because you were exhausted.

Thank you my mentor,
Then we should make a sentence of such quality, is it all right with you?
She had worked so hard, four hours straight without a minute’s rest, that, by noon, she was exhausted and bathed in sweat.
I think this sentence is okay to show two separate results, then.
regards

Yes, that sentence is fine.

thanks a lot
regards