How do we solve the following Diophantine equation?
Find the number of positive integer solutions to $x_1x_2x_3x_4 = 3^{11}\cdot5^{9}\cdot7^{7}\cdot11^{5}$ where $x_1 \le x_2\le x_3\le x_4$.
For equations involving sums, that's easy, but for products, I have no idea. Any idea or suggestion will be welcome! Thanks in advance!