Sure, let's solve the expression step-by-step given [tex]\( c = -4 \)[/tex] and [tex]\( d = 10 \)[/tex].
We need to evaluate:
[tex]\[ \frac{1}{4}\left(c^3+d^2\right) \][/tex]
1. Calculate [tex]\(c^3\)[/tex]:
[tex]\[
c^3 = (-4)^3 = -4 \times -4 \times -4 = -64
\][/tex]
2. Calculate [tex]\(d^2\)[/tex]:
[tex]\[
d^2 = 10^2 = 10 \times 10 = 100
\][/tex]
3. Add the results of [tex]\(c^3\)[/tex] and [tex]\(d^2\)[/tex]:
[tex]\[
c^3 + d^2 = -64 + 100 = 36
\][/tex]
4. Multiply the sum by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} \times 36 = 9
\][/tex]
Therefore, the value of the expression is [tex]\( 9 \)[/tex].
The correct answer is:
[tex]\[
\boxed{9}
\][/tex]
