D&C 121

The Prophet Joseph Smith was inspired to write that -

"...the rights of the priesthood are inseparably connected with the powers of heaven, and that the powers of heaven cannot be controlled nor handled only upon the principles of righteousness."  (Doctrine and Covenants | Section 121:36)

In my mind, the "powers of heaven" is power that comes through the priesthood.  The rights associated with that priesthood to administer that power then can only be done so through principles of righteousness.  In other words, priesthood power or powers of heaven are one of the same and comes from holiness, faith, and righteousness.

Principles of righteousness include where -

"No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned;
42 By kindness, and pure knowledge..."  (Doctrine and Covenants | Section 121:41 - 42)

Where pure knowledge comes as we -

"Let thy bowels also be full of charity towards all men, and to the household of faith, and let virtue garnish thy thoughts unceasingly; then shall thy confidence wax strong in the presence of God; and the doctrine of the priesthood shall distil upon thy soul as the dews from heaven."  (Doctrine and Covenants | Section 121:45)

Actions by which the powers of heaven cannot be administered include where  -

"...their hearts are set so much upon the things of this world, and aspire to the honors of men..."  (Doctrine and Covenants | Section 121:35)

Also where -

"...we undertake to cover our sins, or to gratify our pride, our vain ambition, or to exercise control or dominion or compulsion upon the souls of the children of men, in any degree of unrighteousness..."  (Doctrine and Covenants | Section 121:37)

As we come to understand and live the principles of righteousness, avoiding any works that limit the powers of heaven, the promises are -

"The Holy Ghost shall be thy constant companion, and thy scepter an unchanging scepter of righteousness and truth; and thy dominion shall be an everlasting dominion, and without compulsory means it shall flow unto thee forever and ever."  (Doctrine and Covenants | Section 121:46)

This is the powers of heaven.