To solve the expression \( 16728 : 204 \cdot (328 - 4267 : 17) : 11 - 419 \), we'll break it down step by step.
First, we calculate \( 4267 : 17 \): \[ 4267 \div 17 = 251 \]
Now replace \( 4267 : 17 \) with \( 251 \) in the expression: \[ 16728 : 204 \cdot (328 - 251) : 11 - 419 \]
Next, calculate \( 328 - 251 \): \[ 328 - 251 = 77 \]
Now replace \( (328 - 251) \) with \( 77 \): \[ 16728 : 204 \cdot 77 : 11 - 419 \]
Calculate \( 16728 : 204 \): \[ 16728 \div 204 = 82 \]
Now replace \( 16728 : 204 \) with \( 82 \): \[ 82 \cdot 77 : 11 - 419 \]
Now calculate \( 82 \cdot 77 \): \[ 82 \cdot 77 = 6314 \]
Now replace \( 82 \cdot 77 \) with \( 6314 \): \[ 6314 : 11 - 419 \]
Calculate \( 6314 : 11 \): \[ 6314 \div 11 = 575.8181\ldots \text{ (approximately) } \]
Now replace \( 6314 : 11 \) with \( 575.8181\ldots \): \[ 575.8181 - 419 \]
Finally, perform the subtraction: \[ 575.8181 - 419 = 156.8181 \]
Thus, the final result is approximately:
\[ \boxed{156.82} \]
(rounded to two decimal places).
