To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the numerator:
3⁴ × 57 - 9² × 21

3⁴ means 3 raised to the power of 4, which is 3 × 3 × 3 × 3 = 81.
So, the numerator becomes:
81 × 57 - 9² × 21

9² means 9 raised to the power of 2, which is 9 × 9 = 81.
So, the numerator further simplifies to:
81 × 57 - 81 × 21

Now, let's simplify the denominator:
3⁵ means 3 raised to the power of 5, which is 3 × 3 × 3 × 3 × 3 = 243.

So, the expression becomes:
(81 × 57 - 81 × 21) / 243

Now, let's calculate the numerator:
81 × 57 = 4617
81 × 21 = 1701

So, the numerator simplifies to:
4617 - 1701 = 2916

Finally, let's divide the numerator by the denominator:
2916 / 243 = 12

Therefore, the value of the expression is 12.