Consider the expression (16−12)2+5(8+22)53−(1+4)2
. What is the simplified numerator?(1 point)
Responses
42+60
4 squared plus 60
76
76
54
54
100
100
To find the simplified numerator of the given expression, we must first calculate the expression within the numerator. The given expression is:
(16−12)² + 5(8+22)5³ − (1+4)²
Here's the simplification step by step:
1. Simplify the terms within parentheses:
- (16−12) becomes 4
- (8+22) becomes 30
- (1+4) becomes 5
2. Calculate the values of the exponents and multiplications:
- 4² is equal to 16 (since 4 * 4 = 16)
- 5(30) is equal to 150 (since 5 * 30 = 150)
- 5³ is equal to 125 (since 5 * 5 * 5 = 125)
- 5² is equal to 25 (since 5 * 5 = 25)
3. Substitute the simplified values back into the expression:
16 + (150 * 125) − 25
4. Perform the multiplication:
- 150 * 125 equals 18,750
5. Add and subtract the simplified values:
- 16 + 18,750 - 25
6. Perform the addition and subtraction:
- 18,766 - 25 equals 18,741
The numerator of the original expression, when simplified, equals 18,741. This result is not reflected in the given options, so there might be a misunderstanding or typo in the provided expression or options. If one of the options should indeed represent the correct answer, please provide the correct expression, and I will calculate it for you.