The problem given is:

$a = 9 \quad \text{and} \quad b = 2$

You need to calculate the value of:

$\frac{a}{b} - a^b$

Let's break this down step by step:

1. Calculate $\frac{a}{b}$:

   $\frac{9}{2} = 4.5$

2. Calculate $a^b$:

   $9^2 = 81$

3. Subtract $a^b$ from $\frac{a}{b}$:

   $4.5 - 81 = -76.5$

So, the final answer is:

$\boxed{-76.5}$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:

1. What is the general formula for calculating $a^b$ and how does it differ when $b$ is a negative integer?
2. How does the expression change if $b$ were a fraction instead of an integer?
3. Can you explain the difference between arithmetic operations and exponentiation?
4. How would the expression $\frac{a}{b} - a^b$ change if both $a$ and $b$ were negative?
5. How do you interpret and solve similar expressions when $a$ and $b$ are variables instead of constants?

Tip: When subtracting large numbers, double-check your calculations to avoid simple mistakes.