Use the Product Rule of Exponents to simplify the expression 3 to the power of 8 ⋅3 to the power of 3 .

Answer 1

To simplify the expression \( 3^8 \cdot 3^3 \) using the Product Rule of Exponents, we use the property that states:

\[ a^m \cdot a^n = a^{m+n} \]

In this case, \( a = 3 \), \( m = 8 \), and \( n = 3 \). Applying the Product Rule:

\[ 3^8 \cdot 3^3 = 3^{8+3} = 3^{11} \]

Thus, the simplified expression is:

\[ 3^{11} \]