Can you give a biblical example of how the apostles used this "power"?
Acts 5:12-16. 12The apostles performed many signs and wonders among the people. And all the believers used to meet together in Solomon’s Colonnade. 13 No one else dared join them, even though they were highly regarded by the people. 14 Nevertheless, more and more men and women believed in the Lord and were added to their number. 15 As a result, people brought the sick into the streets and laid them on beds and mats so that at least Peter’s shadow might fall on some of them as he passed by. 16 Crowds gathered also from the towns around Jerusalem, bringing their sick and those tormented by impure spirits, and all of them were healed.
Acts 8:4-7 4Those who had been scattered preached the word wherever they went. 5 Philip went down to a city in Samaria and proclaimed the Messiah there. 6 When the crowds heard Philip and saw the signs he performed, they all paid close attention to what he said. 7 For with shrieks, impure spirits came out of many, and many who were paralyzed or lame were healed. 8 So there was great joy in that city.
There are way too many examples to list here. Suffice it to say that as they went about their daily lives they were ordaining people, hearing their confessions and absolving them of their sins, baptizing them, and on Sunday leading the faithful in worship. All this done by the authority, by the power given to them by Jesus Christ as is clearly mentioned in the Scriptures.
It is impossible to talk about the forgiveness of sins without bringing the sacrificial death of Christ into the picture.
Of course that is what makes everything possible, but what you said ("And where these have been forgiven, sacrifice for sin is no longer necessary. (Heb. 10:14–18)") is not what we were talking about, like some other sacrifice was needed as you seemed to be thinking. I were talking specifically about them having authority and thus the power to do things.