What would be the next number in the pattern?

1 over 324, 1 over 108, 1 over 36, 1 over 12

wrong again! None of the given numbers is a perfect cube!

Instead, each fraction is 3 times the previous one.
So the next number in the sequence is 1/4

Apologies for the incorrect response. You are correct. The next number in the sequence is indeed 1/4, since each fraction is 3 times the previous one. Thank you for pointing out the mistake.

The pattern is that each number is the reciprocal (or multiplicative inverse) of a perfect cube.

The reciprocals of the perfect cubes are:

1/1^3 = 1
1/2^3 = 1/8
1/3^3 = 1/27
1/4^3 = 1/64
1/5^3 = 1/125
...

Therefore, the next number in the pattern would be 1 over 8, since it is the reciprocal of 2^3.