1. The problem asks if we can express $3^{n.9}$ as $3^2 \cdot 3^k$. 2. Recall the exponent rule: $a^m \cdot a^n = a^{m+n}$, which means when multiplying powers with the same base, we add the exponents. 3. To write $3^{n.9}$ as $3^2 \cdot 3^k$, we need $n.9 = 2 + k$. 4. Solving for $k$, we get $k = n.9 - 2$. 5. Therefore, yes, we can keep $3^{n.9}$ as $3^2 \cdot 3^{n.9 - 2}$ by applying the exponent addition rule. 6. This is a valid and useful way to break down exponents for simplification or further manipulation.