Many non-native speakers says:
Someone has a good / bad memory power.
Someone has a good / bad memory.
Which is more appropriate to native speakers?
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"Memory" is, by definition, a kind of "power", at least in the sense of "ability":
memory (n): The faculty by which the mind stores and remembers information.
"Memory power" is therefore redundant and not normally idiomatic:
He has a good memory for faces
If you want to use the word "power" then the "power of recollection" would be fine (often used in the plural):
He has amazing powers of recollection when it comes to the details of his childhood.