Sure! Let's walk through the evaluation of the expression step by step.
Given the expression:
[tex]\[
\frac{1}{4}\left(c^3+d^2\right)
\][/tex]
We need to find the value of this expression when [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex].
1. Calculate [tex]\(c^3\)[/tex]:
[tex]\[
c = -4
\][/tex]
[tex]\[
c^3 = (-4)^3 = -64
\][/tex]
2. Calculate [tex]\(d^2\)[/tex]:
[tex]\[
d = 10
\][/tex]
[tex]\[
d^2 = 10^2 = 100
\][/tex]
3. Add the results from steps 1 and 2:
[tex]\[
c^3 + d^2 = -64 + 100 = 36
\][/tex]
4. Multiply the result by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} \cdot 36 = 9
\][/tex]
So, the value of the expression when [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex] is:
[tex]\[
9
\][/tex]
Thus, the correct answer is:
B. 9
