power / potency
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power
In mathematics, the result of multiplying a number by itself several times. The exponent indicates how many times the number is used as a factor.
Zehn hoch drei ist die dritte Potenz von zehn und ergibt tausend.
Ten to the power of three is the third power of ten and equals one thousand.
You can recognize the meaning of 'Potenz' (power/potency) from the context. Numbers and the word 'hoch' (to the power of) point to mathematics. Adjectives like 'wirtschaftlich' (economic) or 'politisch' (political) point to power. Medical terms like 'D12' or 'C30' belong to pharmacy.
Die politische Potenz dieser kleinen Partei wird oft unterschätzt.
The political power of this small party is often underestimated.
In mathematics, 'Potenz' (power) is often used with the preposition 'von' (of) or in the construction 'etwas zur Potenz erheben' (to raise something to a power). The number that is raised to a power is called the 'Basis' (base).
Der Lehrer erklärte, wie man eine Zahl zur dritten Potenz erhebt.
The teacher explained how to raise a number to the third power.
In the meaning of 'Macht' (power) or 'Fähigkeit' (ability), 'Potenz' is almost always accompanied by an adjective that specifies the area. Common phrases are 'wirtschaftliche Potenz' (economic power), 'finanzielle Potenz' (financial capacity), and 'schöpferische Potenz' (creative power).
Das Unternehmen hat nicht die finanzielle Potenz, um die Konkurrenz zu übernehmen.
The company does not have the financial capacity to take over the competition.
The meaning related to dilution is purely technical language from pharmacy and especially homeopathy. It is practically not used in everyday language.
Dieses homöopathische Mittel ist in der Potenz C30 erhältlich.
This homeopathic remedy is available in the potency C30.
strength / force
'die Kraft' and 'die Potenz' can both express that someone or something is capable or powerful. 'Kraft' is much more natural in everyday language and can mean physical strength, inner strength, or an active energy. In this general meaning, 'Potenz' sounds rather elevated or technical. It is used, for example, for economic, political, or intellectual strength. For normal situations like sports, tiredness, or emotional strain, 'Kraft' almost always fits better. 'Potenz' is more precise when you want to emphasize a particular capacity in a specific area.
Die wirtschaftliche Potenz der Stadt zeigt sich in vielen neuen Firmen.
The city's economic power is reflected in many new companies.
Nach der langen Krankheit hat sie langsam wieder Kraft bekommen.
After the long illness, she slowly regained her strength.