Power
as it it used in this verse,
comes from a Greek word;
used in the Bible with the meanings,

"...Force (literally or figuratively,); specifically miraculous power; (usually by implication, the miracle itself):--ability, abundance, meaning, might, mightily, mighty, mighty deed,
worker of miracle (-s), power,
strength; violence, mighty
(wonderful) work..."

Abingdon's Strong's  
Exhaustive Concordance   
of the Bible    


...God anointed Jesus of Nazareth
with the Holy Ghost and with power:
who went about doing good,
and healing all that were
oppressed
of the devil;
for God was
with Him.

Acts 10:38

Other verses in which  the word 'power'
is used with the above meaning:

Mat 6:13, 22:29;
Mark 9:1, 12:24, 13:26, 14:62
Luke 1:17, 1:35, 4:14, 9:1, 10:19, 21:27, 22:69, 24:49
Acts 1:8; 3:12, 4:7, 4:33, 6:8, 8:10, 10:38
Rom 1:4, 1:16, 1:20, 9:17, 15:13, 15:19
I Cor 1:18, 1:24, 2:4, 2:5, 4:19 4:20, 5:4, 6:12, 6:14, 15:24, 15:43
II Cor 4:7, 6:7, 8:3, 12:9, 13:4, 13:10
Eph 1:19, 3:7, 3:20
Phil 3:10
I Thes 1:5, 2:9
II Tim 1:7, 1:8, 3:5
Heb 1:3, 7:16
I Pet 1:5   II Pet 1:3, 1:16
Rev 4:11, 5:12, 7:12, 11:17, 13:2,    
15:8, 17:13, 19:1