Answer :

Formula:- if a^{m} = a^{n}, then m = n.

N(A) = Number of elements in set A

P(A) = Power Set of A = Set of all the sets possible by the elements of A.

For Example, Let A = {1, 2, 3}

Then, P(A) = {Ø, (1), (2), (3), (1, 2), (2, 3), (3, 1), (1, 2, 3)}

So there are 8 sets in the power set of A.

We know that n[P(A)] = Number of elements in the power set of A.

If n is the number of elements in A, the number of elements in the power set of A = 2^{n}

Given: n[p(a)] = 64

Let the number of elements in set A = x

Then, n(p(a)) = 2^{x}

Therefore, 2^{x} = 64

2^{x} = 2^{6}

x = 6

Hence, n(a) = 6

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