After Jesus cast an unclean devil out of a man in a synagogue service, the people cried, "What a word is this! for with authority and power he commandeth the unclean spirits, and they come out" (Luke 4:36And they were all amazed, and spake among themselves, saying, What a word is this! for with authority and power he commandeth the unclean spirits, and they come out.
See All...). Many bibles will take passages that refer to "power" and change it to "authority." However, here we see the importance of both. Authority is the right to do something. Power is the ability to do something or to make something happen. Among men, a person can have one without the other. A man may have a position that gives him the right to make a decision (the authority), but he may not have the power to make it happen. On the other hand, some people have the power to do certain things even when they do not have the proper authority to do them.

God's power always comes with the proper authority because He has the right to do whatever He wills to do. However, if He has authority without the power to follow through, He is a limited god. That is why changing power to authority as the NIV does in John 17:2As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him.
See All... is such a serious matter. Instead of Jesus having "power over all flesh" (KJB), Jesus has "authority over all people" (NIV). This verse deals with the giving of eternal life. But what if Jesus has the authority (right) to give eternal life, but not the power (ability)? Then we have a serious problem. Being the Son of God, He will have the authority if He has the power. Do not remove the power of the Son and weaken it to simple authority.