Question

If n[P(A)] = 1024 find n(A)

Answer 1

A is a set containing some elements.
P(A) = set of all subsets of A = power set of A.
n(A) = cardinality of A
n[ P(A) ] = cardinality of P(A)

if a set A has m elements then P(A) has 2^m elements ...
so   n[ P(A) ] = 2^m  = 1024 = 2^10
       so  n(A) = 10