Some experts in the law of Moses and Pharisees brought [to Him] a woman who had been caught committing an immoral sexual act and stood her in the middle of the group.

By what power

When He had come into the Temple, the leading priests and elders of the [Jewish] people came to Him while He was teaching, and said, "By what authority are you doing these things [i.e., miracles and teaching]? And who gave you this authority?"

and said, "By what authority are you doing these things [i.e., miracles and teaching]? Or who gave you the authority to do these things?"

So, the Jews asked Him, "What [miraculous] sign will you show us, since you are doing these things [i.e., disrupting their merchandising activities]?"

By what name

we want you men and all the people of Israel to know that this man was made completely well through the name of Jesus Christ from Nazareth. [He is the One] whom you people put to death on the cross, but God raised from the dead.

"We strictly commanded you not to teach in this name [i.e., the name of Jesus] and look [what you have done]; you have filled Jerusalem with your teaching and you intend to hold us responsible for this man's [i.e., Jesus'] death."

General references

And when people bring you in front of synagogue assemblies and rulers and authorities [i.e., for judgment], do not worry about how to speak or what you should say.