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

First, let's simplify the exponents:
(3/2)⁷ = (3⁷)/(2⁷) = 2187/128
(7/2)⁵ = (7⁵)/(2⁵) = 16807/32

Now, let's substitute these values back into the expression:
(2187/128) ÷ (16807/32) + 3/2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(2187/128) * (32/16807) + 3/2

Simplifying the fractions:
(2187 * 32) / (128 * 16807) + 3/2

Multiplying:
69984 / 2158592 + 3/2

To add fractions, we need a common denominator:
(69984 + 3 * 1079296) / (2158592)

Multiplying:
(69984 + 3237888) / (2158592)

Adding:
3307872 / 2158592

Simplifying the fraction:
1653936 / 1079296

The final simplified expression is 1653936/1079296, which can be further reduced if necessary.