mächtig
powerful
Having a lot of power and influence.
Der Vorstandsvorsitzende ist eine mächtige Figur in der Wirtschaftswelt.
The CEO is a powerful figure in the business world.

powerful / mighty
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powerful
Having a lot of power and influence.
Der Vorstandsvorsitzende ist eine mächtige Figur in der Wirtschaftswelt.
The CEO is a powerful figure in the business world.

The adjective 'mächtig' (powerful) is derived directly from the noun 'die Macht' (power). The ending '-ig' turns the noun into an adjective.
Der König war ein sehr mächtiger Mann.
The king was a very powerful man.
When 'mächtig' (powerful) describes people, organizations, or countries, it means 'influential'. When it describes things, forces of nature, or feelings, however, it means 'large', 'strong', or 'intense'.
Das Unternehmen ist ein mächtiger Konkurrent auf dem Weltmarkt.
The company is a powerful competitor on the global market.
In the meaning of 'large' or 'strong', 'mächtig' (mighty/powerful) is often combined with natural phenomena or impressive objects. Typical phrases are 'ein mächtiger Baum' (a mighty tree), 'ein mächtiger Fluss' (a mighty river), or 'ein mächtiger Eindruck' (a powerful impression).
Vor uns stand eine mächtige alte Eiche.
A mighty old oak tree stood before us.
In colloquial speech, 'mächtig' (really/very) is used as an adverb to intensify a feeling or state, similar to 'sehr' (very). In this function, it is not declined.
Ich habe heute mächtig Durst.
I'm really thirsty today.
very
'sehr' and 'mächtig' can both be used as intensifiers. 'sehr' is neutral and suitable in almost any situation. 'mächtig' in this meaning is colloquial and sounds more forceful. It is often used when something is strongly felt, for example anger, hunger, joy, or pride. In formal texts, 'sehr' is more natural. 'mächtig' fits better in casual language when the statement should sound more vivid.

Nach der Arbeit bist du mächtig hungrig, weil du kein Mittagessen hattest.
After work, you are really hungry because you had no lunch.
Beim Gespräch hört der Verkäufer dem Kunden sehr genau zu.
During the conversation, the salesperson listens very carefully to the customer.