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Why was the union of Brandenburg and Prussia important to the Hohenzollerns?

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Historical map showing the unification of Germany by Prussia in the late 19th century. The map highlights in green the Kingdom of Prussia as of 1866, and in yellow the additional territories that formed the German Empire by 1871-1918, encompassing most of north-central Europe. Neighboring countries such as France, Belgium, the Netherlands, Denmark, Sweden, Russia, Austria-Hungary, and Switzerland are labeled, with major regions and states within the empire clearly marked. — Prussia The unification of Germany by Prussia, which brought most of north-central Europe into one kingdom.

The union of Brandenburg and Prussia was fundamental to the rise of the Hohenzollern dynasty as a major European power. This consolidation provided the dynastic nucleus upon which the kingdom of Prussia was built.123

The importance of this union for the Hohenzollerns included:

Sovereignty and Status: By acquiring the duchy of Prussia in 1618, the electors of Brandenburg gained a territory that eventually allowed them to secure the royal title of "king in Prussia" in 1701, as this land lay outside the jurisdiction of the Holy Roman Empire.1
Military and Administrative Strength: The Great Elector, Frederick William, utilized the combined resources of these territories to establish a centralized administration, a professional army, and a sound fiscal basis, transforming the state into a significant European power.21
Territorial Expansion: The union created a base for further expansion, enabling the dynasty to pursue dynastic objectives, such as the acquisition of Silesia and participation in the partitions of Poland, which significantly enhanced their influence and resources.41