We can rewrite $27^8$ as $(3^3)^8$ and $9^q$ as $(3^2)^q$.
Using the property $(a^m)^n = a^{mn}$, we can simplify the equation to $3^{3 \cdot 8} = 3^{2q}$.
This means that $3^{24} = 3^{2q}$.
Since the bases are the same, we can set the exponents equal to each other:
$24 = 2q$.
Dividing both sides by 2, we find that $q = \boxed{12}$.
The answer is: 12
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of $q$ if $27^8 = 9^q$?

### Answer:
