To simplify the expression \( \frac{3^3 \times 3^3}{3^4} \), we can use the properties of exponents.
First, we know that when multiplying like bases, we add the exponents:
\[ 3^3 \times 3^3 = 3^{3+3} = 3^6 \]
Next, we can substitute that back into the expression:
\[ \frac{3^6}{3^4} \]
When dividing like bases, we subtract the exponents:
\[ 3^{6-4} = 3^2 \]
Now, we can evaluate \( 3^2 \):
\[ 3^2 = 9 \]
None of the provided choices (30, 31, 32, 34) include 9, and since \( 9 \) is not listed among the choices, it appears there may have been a misunderstanding in the options. However, the simplified expression for the given mathematical operation is indeed \( 9 \). If you have any further questions or if there's more context to this problem, please let me know!