To solve the expression \((−35)×(516)×(712)÷(−316)×(−57)\), we will follow the order of operations and the rules for multiplication and division.
First, let's break down and simplify the expression step by step. We can group the multiplication and division to make it easier to handle:
\[ (−35) \times (516) \times (712) \div (−316) \times (−57) \]
Since we are dividing by a negative number, we can rewrite the expression as follows:
\[ (−35) \times (516) \times (712) \times \left(\frac{1}{−316}\right) \times (−57) \]
We can also rearrange the multiplication and division because multiplication is commutative:
\[ (−35) \times (−57) \times (516) \times (712) \div (−316) \]
Now we can compute \( (−35) \times (−57) \):
\[ (−35) \times (−57) = 1995 \]
Now substitute this back into the expression:
\[ 1995 \times (516) \times (712) \div (−316) \]
Next, we can compute \( 1995 \times (516) \):
\[ 1995 \times 516 = 1,031,220 \]
Now substitute this into the expression:
\[ 1,031,220 \times (712) \div (−316) \]
Next, calculate \( 1,031,220 \times (712) \):
\[ 1,031,220 \times 712 = 734,337,840 \]
Now substitute this into the expression:
\[ 734,337,840 \div (−316) \]
Finally, compute \( 734,337,840 \div (−316) \):
\[ 734,337,840 \div (−316) \approx -2,322,000 \]
So the final result is:
\[ \boxed{-2,322,000} \]
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