Me da mucha energía , sería la forma correcta de decir la oración.

Me da mucha energia, ó me da muchas energías; you can say it in plural or singular form.

me da muchos energías = Not Correct Because "Energía" is a female noun. Try to remember that in spanish, Noun must match in number and gender with adjectives. So in this case the right way is : Mucha Energía. (A singular female adjective plus a female noun) Muchas energías is not possible because "Energía" is a non countable noun. You wont listen... "Dame una, tres o mil energías). You give all the energy or nothing.

Say: Me da mucha energía.

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