To simplify the expression √25/81 × 16/49 × 196/9, we can follow these steps:

Step 1: Simplify each fraction individually:
√25/81 = √(5^2)/(9^2) = 5/9
16/49 = 16/49
196/9 = 196/9

Step 2: Multiply the simplified fractions together:
(5/9) × (16/49) × (196/9) = (5 × 16 × 196) / (9 × 49 × 9)

Step 3: Simplify the numerator and denominator:
(5 × 16 × 196) / (9 × 49 × 9) = (5 × 16 × 196) / (9^2 × 49)
= (5 × 16 × 196) / (81 × 49)
= (5 × 16 × 196) / 3969

Step 4: Calculate the numerator:
5 × 16 × 196 = 15680

Step 5: Substitute the numerator and denominator back into the expression:
(5 × 16 × 196) / 3969 = 15680 / 3969

Therefore, the simplified expression is 15680/3969.