To simplify \( 3^5 \cdot 3^7 \) using the Product Rule of Exponents, we can combine the exponents since the bases are the same.
The Product Rule states that when multiplying two exponential expressions with the same base, you add the exponents:
\[ a^m \cdot a^n = a^{m+n} \]
In this case, our base \( a \) is \( 3 \), \( m \) is \( 5 \), and \( n \) is \( 7 \). So we add the exponents:
\[ 3^5 \cdot 3^7 = 3^{5 + 7} = 3^{12} \]
Thus, \( 3^5 \cdot 3^7 \) simplifies to \( 3^{12} \).
The correct response is:
3 to the 12th power (312).