Let's begin by plugging in the given values [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex] into the expression [tex]\(\frac{1}{4}(c^3 + d^2)\)[/tex].
1. Calculate [tex]\(c^3\)[/tex]:
[tex]\[ c^3 = (-4)^3 = -64 \][/tex]
2. Calculate [tex]\(d^2\)[/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. Now, multiply the result by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{4}(c^3 + d^2) = \frac{1}{4}(36) = 9 \][/tex]
So, the value of the expression is [tex]\(9\)[/tex].
Therefore, the correct answer is:
B. 9
