Answer :
To evaluate the expression [tex]\(\frac{x^5 - x}{4y}\)[/tex] when [tex]\(x = -4\)[/tex] and [tex]\(y = 4\)[/tex], let's break down the steps in detail.
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ x = -4, \quad y = 4 \][/tex]
2. Calculate [tex]\(x^5\)[/tex]:
[tex]\[ x^5 = (-4)^5 = -1024 \][/tex]
3. Calculate [tex]\(x^5 - x\)[/tex]:
[tex]\[ x^5 - x = -1024 - (-4) = -1024 + 4 = -1020 \][/tex]
4. Calculate the denominator [tex]\(4 \cdot y\)[/tex]:
[tex]\[ 4 \cdot y = 4 \cdot 4 = 16 \][/tex]
5. Form the fraction:
[tex]\[ \frac{x^5 - x}{4y} = \frac{-1020}{16} \][/tex]
6. Simplify the fraction:
[tex]\[ \frac{-1020}{16} = -63.75 \][/tex]
Hence, the expression [tex]\(\frac{x^5 - x}{4y}\)[/tex] evaluates to [tex]\(-63.75\)[/tex].
Given the answer choices in the problem, none of them directly match [tex]\(-63.75\)[/tex]. But based on the problem structure, let's confirm if the corrected values maybe there under another fraction form:
[tex]\[ -\frac{1023}{4} = -255.75 \quad \text{(incorrect)} \][/tex]
[tex]\[ \frac{1025}{4} = 256.25 \quad \text{(incorrect, positive and different value)} \][/tex]
[tex]\[ \frac{16,385}{4} = 4096.25 \quad \text{(incorrect)} \][/tex]
Correcting, base numeric forms:
\[ None aligns directly in given problem answers; calculation fits additional contextual incorrectly given choice's form. Deduction fits corrected path thus none directly selection preflected-alignment.
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[ x = -4, \quad y = 4 \][/tex]
2. Calculate [tex]\(x^5\)[/tex]:
[tex]\[ x^5 = (-4)^5 = -1024 \][/tex]
3. Calculate [tex]\(x^5 - x\)[/tex]:
[tex]\[ x^5 - x = -1024 - (-4) = -1024 + 4 = -1020 \][/tex]
4. Calculate the denominator [tex]\(4 \cdot y\)[/tex]:
[tex]\[ 4 \cdot y = 4 \cdot 4 = 16 \][/tex]
5. Form the fraction:
[tex]\[ \frac{x^5 - x}{4y} = \frac{-1020}{16} \][/tex]
6. Simplify the fraction:
[tex]\[ \frac{-1020}{16} = -63.75 \][/tex]
Hence, the expression [tex]\(\frac{x^5 - x}{4y}\)[/tex] evaluates to [tex]\(-63.75\)[/tex].
Given the answer choices in the problem, none of them directly match [tex]\(-63.75\)[/tex]. But based on the problem structure, let's confirm if the corrected values maybe there under another fraction form:
[tex]\[ -\frac{1023}{4} = -255.75 \quad \text{(incorrect)} \][/tex]
[tex]\[ \frac{1025}{4} = 256.25 \quad \text{(incorrect, positive and different value)} \][/tex]
[tex]\[ \frac{16,385}{4} = 4096.25 \quad \text{(incorrect)} \][/tex]
Correcting, base numeric forms:
\[ None aligns directly in given problem answers; calculation fits additional contextual incorrectly given choice's form. Deduction fits corrected path thus none directly selection preflected-alignment.
