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

(4/5) x (9/14) x (15/16) = (4 x 9 x 15) / (5 x 14 x 16)
= 540 / 1120
= 27 / 56

Therefore, the product of the fractions 4/5, 9/14, and 15/16 is 27/56.