Consider the expression (16−12)2+5(8+22)53−(1+4)2

The simplified numerator of the expression is 100.

To simplify the numerator of the given expression, we need to perform the operations within parentheses first, then evaluate any exponents, and finally perform any remaining arithmetic operations.

Let's break it down step by step:

1. Evaluate the expression inside the first set of parentheses:
(16 - 12) = 4

2. Evaluate the expression inside the second set of parentheses:
(8 + 22) = 30

3. Evaluate the expression inside the third set of parentheses:
(1 + 4) = 5

4. Evaluate the exponents:
(4^2) = 16

5. Now, let's substitute the values from the previous steps back into the original expression:
(4^2) + 5(30) / 53 - (5^2)

6. Perform the remaining arithmetic operations:
(16) + 5(30) / 53 - (25)
16 + 150 / 53 - 25
16 + 2.83 - 25
18.83 - 25
-6.17

Therefore, the simplified numerator is -6.17.

To simplify the expression, let's break it down step-by-step:

Step 1: Simplify the expression within brackets first:
(16 - 12) = 4
(8 + 22) = 30
(1 + 4) = 5

Step 2: Simplify the exponent:
4^2 = 16

Step 3: Simplify the multiplication and division:
5 * 30 = 150
150 / 53 = 2.83 (approximately)

Step 4: Add up the values:
4 + 16 + 2.83 - 5^2 = 4 + 16 + 2.83 - 25 = 76.83

Therefore, the simplified numerator is 76.83.