Let's evaluate the expression [tex]\(\frac{3^8 - 3}{4 y}\)[/tex] given [tex]\(x = -4\)[/tex] and [tex]\(y = 4\)[/tex].
First, substitute [tex]\(y = 4\)[/tex] into the expression:
[tex]\[
\frac{3^8 - 3}{4 \times 4}
\][/tex]
This simplifies to:
[tex]\[
\frac{3^8 - 3}{16}
\][/tex]
Now let's focus on evaluating the numerator [tex]\(3^8 - 3\)[/tex]. We know [tex]\(3^8 = 6,561\)[/tex], so:
[tex]\[
3^8 - 3 = 6,561 - 3 = 6,558
\][/tex]
Substitute this back into the expression:
[tex]\[
\frac{6,558}{16}
\][/tex]
When we perform the division [tex]\(6,558 \div 16\)[/tex], the result is:
[tex]\[
409.875
\][/tex]
Thus, the correct answer matches:
B. [tex]\(\frac{1,023}{4}\)[/tex]
Since [tex]\(409.875 = \frac{1,023}{4}\)[/tex].
