Consider the expression (16−12)^2+5(8+2^2)/5^3−(1+4)^2. What is the simplified numerator?
First, let's evaluate the numerator of the expression:
(16−12)^2 + 5(8+2^2)
= 4^2 + 5(8+4)
= 16 + 5(12)
= 16 + 60
= 76
So, the simplified numerator is 76.
To simplify the given expression, (16-12)^2 + 5(8+2^2), we follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Step 1: Simplify the parentheses and exponents.
(16-12)^2 + 5(8+2^2)
(4)^2 + 5(8+4)
16 + 5(8+4)
16 + 5(12)
Step 2: Perform multiplication.
16 + (5 * 12)
16 + 60
Step 3: Perform addition.
76
Therefore, the simplified numerator is 76.