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Select the correct answer.

Evaluate the following expression when [tex]x = -4[/tex] and [tex]y = 4[/tex].
[tex]\[ \frac{3^8 - 3}{4y} \][/tex]

A. [tex]\(\frac{16,395}{4}\)[/tex]
B. [tex]\(\frac{1,023}{4}\)[/tex]
C. [tex]\(\frac{1,025}{4}\)[/tex]
D. [tex]\(-\frac{1,023}{4}\)[/tex]



Answer :

GinnyAnswer
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].

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