To simplify the expression 72^3 * 54^2 / 108^4, we can break it down step by step.

First, let's simplify the numerator:
72^3 = 72 * 72 * 72 = 373,248

Next, let's simplify the denominator:
54^2 = 54 * 54 = 2,916
108^4 = 108 * 108 * 108 * 108 = 1,188,961,344

Now, we can rewrite the expression as:
373,248 / 2,916 / 1,188,961,344

To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as:
373,248 * 1,188,961,344 / 2,916

Now, we can simplify the expression further by dividing:
373,248 * 1,188,961,344 = 443,861,759,457,312

443,861,759,457,312 / 2,916 = 152,249,999,999

Therefore, 72^3 * 54^2 / 108^4 simplifies to 152,249,999,999.