To find the power set of ( B = {-4, 0, 4} ), we need to list all possible subsets of ( B ). The power set of a set ( B ) includes every subset of ( B ), including the empty set and ( B ) itself.

Given ( B = {-4, 0, 4} ), the subsets of ( B ) are as follows:

1. The empty set: (\emptyset)
2. Subsets with one element:

• ({-4})
• ({0})
• ({4})

1. Subsets with two elements:

• ({-4, 0})
• ({-4, 4})
• ({0, 4})

1. The subset with all three elements:

• ({-4, 0, 4})

So, the power set ( \mathcal{P}(B) ) of ( B ) is:

[ \mathcal{P}(B) = {\emptyset, {-4}, {0}, {4}, {-4, 0}, {-4, 4}, {0, 4}, {-4, 0, 4}} ]

The power set contains ( 2^n ) subsets, where ( n ) is the number of elements in the original set. Here, ( n = 3 ), so the power set contains ( 2^3 = 8 ) subsets, which matches our list.