To find the product of \( \frac{2}{9} \) and \( \frac{5}{7} \), you multiply the numerators and the denominators together:
\[ \frac{2}{9} \times \frac{5}{7} = \frac{2 \times 5}{9 \times 7} = \frac{10}{63} \]
So, the product of \( \frac{2}{9} \) and \( \frac{5}{7} \) is \( \frac{10}{63} \).