A.T. Robertson Commentary Romans 8:11

"But if the Spirit of him that raised up Jesus from the dead dwelleth in you, he that raised up Christ Jesus from the dead shall give life also to your mortal bodies through his Spirit that dwelleth in you." — Romans 8:11 (ASV)

Shall quicken (ζωοποιησε). Future active indicative of ζωοποιεω, late verb from ζωοποιος, making alive. See on 1 Corinthians 15:22.

Through his Spirit (δια του πνευματος). B D L have δια το πνευμα (because of the Spirit). Both ideas are true, though the genitive is slightly more probably correct.