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To solve this expression, we will follow the order of operations (PEMDAS/BODMAS). First, we will deal with the division and multiplication from left to right:
(-3) ÷ (34) = -3/34 ≈ -0.0882
-0.0882 × 27 = -2.3826
-2.3826 × (-516) = 1229.3656
Lastly, we can divide 1229.3656 by 57:
1229.3656 ÷ 57 ≈ 21.5748
Therefore, the value of the expression is approximately 21.5748.