To simplify the expression \( \frac{3^3 \times 3^3}{3^4} \), we can follow the rules of exponents.
First, we can simplify the numerator:
- \(3^3 \times 3^3 = 3^{3+3} = 3^6\) (using the property that when multiplying like bases, you add the exponents).
Now, our expression looks like this:
\( \frac{3^6}{3^4} \)
Next, we can simplify the fraction. According to the rules of exponents, when dividing like bases, we subtract the exponents:
- \(3^6 \div 3^4 = 3^{6-4} = 3^2\)
Therefore, the simplified expression is:
\(3^2\)
Finally, calculating \(3^2\) gives us:
\(9\)
In summary, the simplified expression for \( \frac{3^3 \times 3^3}{3^4} \) is:
9