Give him praise for his acts of power: give him praise in the measure of his great strength.

Praise Him for His mighty acts; Praise Him according to His abundant greatness.

Praise him for his mighty acts - See the notes at Psalm 145:4 : "One generation shall praise thy works to another, and shall declare thy mighty acts." The Hebrew word is the same. The reference is to that which displays the power of God; the things which manifest his omnipotence.
Praise him according to his excellent greatness - Hebrew, the multitude of his greatness. Let the praise in elevation correspond with this; let it be such as shall properly express this; let all be employed that will contribute to make this known, or that will be appropriate to this. Hence, the psalmist proceeds to call on all to make use of everything, by instrument and voice, that would in any manner set forth the praise of God.

For his mighty acts - Whether manifested in creation, government, mercy or justice.
His excellent greatness - כרב גדלו kerob gudlo, according to the multitude of his magnitude, or of his majesty. After the manyfoldness of his mickleness - Anglo-Saxon. After the mykelnes of his greathede - Old Psalter. Let the praise be such as is becoming so great, so holy, and so glorious a Being.

Praise him for his mighty acts,.... The creation of all things out of nothing; the sustaining of all beings; the government of the world; the redemption of man by Christ, and the wonderful works done by him on earth; the work of grace upon the hearts of his people, and the preservation of them in grace to glory;
praise him according to his excellent greatness; or, "according to the multitude of his greatness" (t); which appears in his nature, perfections, and work, and these both of providence and grace; and in proportion hereunto, and according to the abilities of creatures, angels, and men, is he to be praised; which is giving him the honour due unto his name; see Psalm 96:8.
(t) "secundum multudinem magnitudinie ejus", V. L. Montanus, Gejerus; so Ainsworth.

mighty acts-- (Psalm 145:4).
excellent greatness--or, abundance of greatness.