Use the exponential rule to simplify the expression. Evaluate all exponential expressions. Assume the variables represent nonzero real numbers.
Given expression:
\( (3^{2} \cdot 3^{5})^{2} \)
Using the exponential rule \( a^{m} \cdot a^{n} = a^{m+n} \), we can simplify the expression as:
\( (3^{2+5})^{2} \)
\( (3^{7})^{2} \)
Now using the exponential rule \( (a^{m})^{n} = a^{mn} \), we can further simplify the expression as:
\( 3^{7 \cdot 2} \)
\( 3^{14} \)
Therefore, the simplified expression is \( 3^{14} \).