(38175:75+1369+47•708-6560:82):38

To simplify the expression \( \frac{38175:75+1369+47\cdot708-6560:82}{38} \), we will follow the correct order of operations (PEMDAS/BODMAS).

1. Division Operations:

   • \( 38175 \div 75 = 509 \)
   • \( 6560 \div 82 = 80 \)

   After performing these divisions, the expression simplifies to: \[ (509 + 1369 + 47 \cdot 708 - 80) : 38 \]

2. Multiplication:

   • \( 47 \cdot 708 = 33396 \)

   So now we have: \[ (509 + 1369 + 33396 - 80) : 38 \]

3. Addition and Subtraction:

   • First, add: \[ 509 + 1369 = 1878 \]
   • Then add: \[ 1878 + 33396 = 35274 \]
   • Finally, subtract: \[ 35274 - 80 = 35234 \]

4. Final Division: Now, we divide by 38: \[ \frac{35234}{38} = 926 \]

Thus, the final result is: \[ \boxed{926} \]