$(5+4-3)^2:(5\times2-10\times1)=$

This simple rule is **the order of operations which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that operations enclosed in parentheses precede all others,**

In the given expression, the establishment of division between two sets of parentheses, **note that the parentheses on the left indicate strength**, therefore, in accordance to the order of operations mentioned above, we start simplifying the expression within those parentheses, and as we proceed, we obtain the result derived from simplifying the expression within those parentheses with given strength, and in the final step, we divide the result obtained from the simplification of the expression within the parentheses on the right,

We proceed similarly with the simplification of the expression within the parentheses on the left, where we perform the operations of multiplication and division, in strength, in contrast, we simplify the expression within the parentheses on the right, which, according to the order of operations mentioned above, means **multiplication precedes division**, hence we first perform the operations of multiplication within those parentheses and then proceed with the operation of division:

$(5+4-3)^2:(5\cdot2-10\cdot1)= \\
(-2)^2:(10-10)= \\
4:0\\$We conclude that** the sequence of operations within the expression that is within the parentheses on the left yields a smooth result, this result we leave within the parentheses,** these we raised in the next step in strength, this means we remember that** every number (positive or negative) in dual strength gives a positive result,**

**As we proceed, note that in the last expression we received from establishing division by the number 0**, this operation is known as **an undefined mathematical operation (and this is the simple reason why a number should never be divided by 0 parts)** therefore, the given expression yields **a value that is not defined**, commonly denoted as **"undefined group"** and use the symbol :

$\{\empty\}$__In summary:__

$4:0=\\
\{\empty\}$__Therefore, the correct answer is answer A.__