To simplify the expression \( 3^8 \cdot 3^3 \) using the Product Rule of Exponents, you add the exponents when multiplying like bases. The Product Rule states:
\[ a^m \cdot a^n = a^{m+n} \]
In this case:
\[ 3^8 \cdot 3^3 = 3^{8+3} = 3^{11} \]
Thus, the simplified expression is:
\[ 3^{11} \]