9/14 x 7/27 carry out indicated operation

To multiply fractions, we simply multiply the numerators together and multiply the denominators together.

Step 1: Multiply the numerators: 9 \times 7 = 63 .
Step 2: Multiply the denominators: 14 \times 27 = 378 .

Therefore, the multiplication of \frac{9}{14} and \frac{7}{27} is equal to \frac{63}{378}=\frac{1}{6} .

Answer: \frac{1}{6}