## Solving the Expression: (81/16) - 3/4 x (25/4) - 3/2 divided by 5/2^-3

This problem involves several arithmetic operations, so we need to follow the order of operations (PEMDAS/BODMAS) to solve it correctly. Let's break it down step-by-step:

**1. Simplify the exponents:**

- 2^-3 = 1/(2^3) = 1/8

**2. Rewrite the division as multiplication:**

- Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, dividing by 5/2^-3 is the same as multiplying by (2^-3)/5.

**3. Apply the order of operations:**

**Multiplication and Division (from left to right):**- 3/4 x (25/4) = 75/16
- (2^-3)/5 = 1/40

**Addition and Subtraction (from left to right):**- (81/16) - 75/16 = 6/16 = 3/8
- 3/8 - 3/2 = -9/8

**4. Perform the final multiplication:**

- (-9/8) x (1/40) = -9/320

**Therefore, the solution to the expression (81/16) - 3/4 x (25/4) - 3/2 divided by 5/2^-3 is -9/320.**