Certainly! Let's simplify the given expression step by step:
The expression we need to simplify is:
[tex]\[
\frac{8|7 + (-10)|}{2 \cdot 3^2}
\][/tex]
### Step 1: Simplify inside the absolute value
First, we handle the expression inside the absolute value:
[tex]\[
7 + (-10) = 7 - 10 = -3
\][/tex]
### Step 2: Apply the absolute value
The absolute value of [tex]\(-3\)[/tex] is:
[tex]\[
| -3 | = 3
\][/tex]
### Step 3: Substitute back into the expression
Next, we substitute this absolute value back into the original expression:
[tex]\[
\frac{8 \times 3}{2 \cdot 3^2}
\][/tex]
### Step 4: Simplify the denominator
Calculate [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
So the denominator becomes:
[tex]\[
2 \cdot 9 = 18
\][/tex]
### Step 5: Simplify the numerator
The numerator simplifies to:
[tex]\[
8 \times 3 = 24
\][/tex]
### Step 6: Divide the numerator by the denominator
Finally, we divide the simplified numerator by the simplified denominator:
[tex]\[
\frac{24}{18} = \frac{4}{3}
\][/tex]
Therefore, the simplified value of the given expression is:
[tex]\[
\boxed{\frac{4}{3}}
\][/tex]
This matches one of the given answer choices.
