Find the number of divisors of $2^{9} \cdot 3^{14}$.
Each divisor is the product of some power of 2 and some power of 3. There are 10 choices for the power of $2\left(2^{0}, 2^{1}, \ldots, 2^{9}\right)$ and 15 choices for the power of $3\left(3^{0}, 3^{1}, \ldots, 3^{14}\right)$, and, since these choices are independent, there are a total of $10 \cdot 15=150$ divisors.