That Jesus had innate power and authority is beyond dispute. However, the NT is at pains to point out that Jesus' "power" δύναμις (dunamis) had two different sources.
- During Jesus' incarnation on earth, He always depended on God for his power to perform miracles and all else. Phil 2:5-8 - "Christ Jesus: Who, existing in the form of God, did not consider equality with God something to be grasped, but emptied Himself, taking the form of a servant, being made in human likeness. And being found in appearance as a man, He humbled Himself and became obedient to death—even death on a cross." It was during Jesus' incarnation on earth that he became tired, hungry and thirsty (John 4:1-42), wept (John 11:1-57), prays for divine strength (John 17), bleads and dies (John 18:12, 19:17-42), etc. That is, Jesus constantly declared Himself subject to His Father and that all His authority and power came from the Father, John 10:18, 10:32, 15:15, Rev 2:26, etc.
Acts 10:38 is simply another reference to the fact that Jesus was given and depended upon His Father for His power during the incarnation.
- After Jesus' incarnation, He is described as having His own power and imparting that to us as Christians, 2 Peter 1:3, 16, 3:4, 1 Peter 1:5, 7, 13, 4:13; Phil 3:20, 21, Col 1:28, 29, 2 Cor 12:8, 9, etc; this will be most apparent when Jesus returns, "in power and great glory" Matt 24:30, Luke 21:17.
The point of this distinction is important. While on earth, Jesus set us an example of how to live by depending on divine power, eg, Conformed to the likeness of the Son, Rom 8:29; Walk as Jesus walked, 1 John 2:6; Forgive as Jesus forgave, Matt 6:12, Eph 4:32.; Be imitators of God, Eph 5:1; Be holy as Jesus is holy, Lev 11:44, 45, 1 Peter 1:15, 16; Be pure as He is pure, 1 John 3:3; Partakers of the divine nature, 2 Peter 1:4; We are being changed into Christ’s glory (= reputation), 2 Cor 3:18; Pray as Jesus prayed, Luke 11:1; We are to have the mind of Christ, Phil 2:5, 1 Cor 2:16; Be kind because God is kind, Luke 6:34, 35; Be merciful because God is merciful, Luke 6:36; Be servants to others as Jesus was, John 13:15-17, 1 Peter 4:11b, Matt 20:24-28; Be patient as Jesus was patient, 1 Tim 1:16; Talk/speak as Jesus speaks, 1 Peter 4:11a; etc.
That is, we are not to live by our own power/ability (as Jesus easily could have) but to live by the example and ability of Jesus.