## Simplifying the Expression: (81/16) - 3/4 x (25/9) - 3/2 divided by 5/2^-3

This problem requires us to follow the order of operations (PEMDAS/BODMAS) to arrive at the correct solution. Let's break down the steps:

### Step 1: Evaluate the exponent

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

### Step 2: Simplify the division

- 5 / (1/8) = 5 * 8 = 40

### Step 3: Perform multiplication

- (3/4) * (25/9) = (3 * 25) / (4 * 9) = 75/36 = 25/12

### Step 4: Simplify the expression

- (81/16) - (25/12) - (3/2) / 40
- To perform addition and subtraction, we need a common denominator. The least common multiple of 16, 12, and 40 is 240.
- (81/16) * (15/15) = 1215/240
- (25/12) * (20/20) = 500/240
- (3/2) * (120/120) = 360/240
- Now we have: (1215/240) - (500/240) - (360/240) / 40
- (1215 - 500 - 360) / 240 = 355/240

### Step 5: Divide by 40

- (355/240) / 40 = (355/240) * (1/40) = 355/9600