To find the correct answer for the given expression [tex]\(\frac{x^5 - x}{4y}\)[/tex] when [tex]\(x = -4\)[/tex] and [tex]\(y = 4\)[/tex], follow these steps:
1. First, substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 4\)[/tex] into the expression:
[tex]\[
\frac{(-4)^5 - (-4)}{4 \cdot 4}
\][/tex]
2. Calculate [tex]\((-4)^5\)[/tex]:
[tex]\[
(-4)^5 = -4 \cdot -4 \cdot -4 \cdot -4 \cdot -4 = -1024
\][/tex]
3. Compute [tex]\((-4)^5 - (-4)\)[/tex]:
[tex]\[
-1024 - (-4) = -1024 + 4 = -1020
\][/tex]
4. Compute the denominator [tex]\(4 \cdot 4\)[/tex]:
[tex]\[
4 \cdot 4 = 16
\][/tex]
5. Evaluate the entire expression:
[tex]\[
\frac{-1020}{16}
\][/tex]
6. Simplify the fraction:
[tex]\[
\frac{-1020}{16} = -63.75
\][/tex]
Now, looking at the given options:
A. [tex]\(\frac{16,385}{4}\)[/tex] which simplifies to [tex]\(4096.25\)[/tex]
B. [tex]\(-\frac{1,023}{4} = -255.75\)[/tex]
C. [tex]\(\frac{3,925}{4} = 981.25\)[/tex]
D. [tex]\(\frac{1,023}{4} = 255.75\)[/tex]
The simplified result of [tex]\(\frac{-1020}{16}\)[/tex] is [tex]\(-63.75\)[/tex], which doesn't directly correspond to any of the fractional forms given in the options.
To make it clear and consistent with our results, none of the options exactly match the value of [tex]\(-63.75\)[/tex]. Hence, if forced to select based on the given options, there seems to be a mistake or mismatch with the result provided and none of the choices directly match [tex]\(-63.75\)[/tex].
