To simplify the expression \( 3^8 \cdot 3^3 \) using the Product Rule of Exponents, we can apply the rule which states that when multiplying two expressions with the same base, we add the exponents.
In this case, the base is \( 3 \). According to the rule:
\[ a^m \cdot a^n = a^{m+n} \]
Therefore, we can write:
\[ 3^8 \cdot 3^3 = 3^{8+3} \]
Now, we add the exponents:
\[ 8 + 3 = 11 \]
So the expression simplifies to:
\[ 3^{11} \]
Thus, the simplified form of \( 3^8 \cdot 3^3 \) is \( 3^{11} \).
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