To determine the value of the expression [tex]\(\frac{1}{4}\left(c^3+d^2\right)\)[/tex] when [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex], follow these steps:
1. Calculate [tex]\(c^3\)[/tex]:
- Given [tex]\(c = -4\)[/tex], we need to find [tex]\((-4)^3\)[/tex].
- [tex]\((-4)^3 = -4 \times -4 \times -4 = -64\)[/tex].
2. Calculate [tex]\(d^2\)[/tex]:
- Given [tex]\(d = 10\)[/tex], we need to find [tex]\(10^2\)[/tex].
- [tex]\(10^2 = 10 \times 10 = 100\)[/tex].
3. Add [tex]\(c^3\)[/tex] and [tex]\(d^2\)[/tex]:
- Combine the results from the previous steps.
- [tex]\(-64 + 100 = 36\)[/tex].
4. Multiply by [tex]\(\frac{1}{4}\)[/tex]:
- We need to find [tex]\(\frac{1}{4} \times 36\)[/tex].
- [tex]\(\frac{1}{4} \times 36 = 9\)[/tex].
So, the value of the expression [tex]\(\frac{1}{4}\left(c^3+d^2\right)\)[/tex] when [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex] is [tex]\(9\)[/tex].
Therefore, the correct answer is:
B. 9
