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Definition of mightiness : 1. Highness; excellency; - with a possessive pronoun, a title of dignity; as, their high mightinesses.
2. The quality of being mighty; possession of might; power; greatness; high dignity.

Synonyms:

business leader, baron, king, great power, major power, magnate, tycoon, mogul, big businessman, exponent, superpower, world power, ability, index, top executive

authority (part of speech: noun)

influence, title, commission, precedence, control, privilege, might, potency, purview, power, strength, credential, punch, superiority, sway, enfranchisement, stature, clout, puissance, charge, kingship, license, steam, seniority, prestige, mastery, powerfulness, prepotency, prerogative, command, authority, right, empowerment, mandate, domination, birthright, primacy, entitlement, rank, sovereignty, faculty, office, force, cogency

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