2/7 * (3 1/2)^2 - 5/13 : 3 1/13 + 9/10 : 3 3/5

1. Convert mixed numbers to improper fractions: 3 1/2 = 7/2, 3 1/13 = 40/13, 3 3/5 = 18/5. The expression becomes: 2/7 * (7/2)^2 - 5/13 : 40/13 + 9/10 : 18/5.

2. Calculate the square: (7/2)^2 = 49/4. The expression is now: 2/7 * 49/4 - 5/13 : 40/13 + 9/10 : 18/5.

3. Perform multiplication and division from left to right: 2/7 * 49/4 = 7/2. 5/13 : 40/13 = 5/13 * 13/40 = 5/40 = 1/8. 9/10 : 18/5 = 9/10 * 5/18 = 45/180 = 1/4.

4. Substitute the results back: 7/2 - 1/8 + 1/4.

5. Find a common denominator (8) and solve: 28/8 - 1/8 + 2/8 = 29/8 = 3 5/8.