Let's simplify the given expression step-by-step:
[tex]\[ 18.35 - (-4)^3 \frac{(13.62 - 8.69)}{32} - 4.08 \][/tex]
### Step 1: Calculate the numerator of the fraction.
First, we need to simplify the expression within the parentheses.
[tex]\[ 13.62 - 8.69 \][/tex]
[tex]\[ 13.62 - 8.69 = 4.93 \][/tex]
So the numerator of the fraction is [tex]\( 4.93 \)[/tex].
### Step 2: Calculate the exponentiation.
Next, we need to calculate [tex]\((-4)^3\)[/tex].
[tex]\[ (-4)^3 = -64 \][/tex]
### Step 3: Calculate the fraction.
Now, we need to multiply the exponentiation result by the numerator and then divide by 32.
[tex]\[ -64 \times \frac{4.93}{32} \][/tex]
First, calculate the fraction part:
[tex]\[ \frac{4.93}{32} = 0.1540625 \][/tex]
Then multiply by [tex]\(-64\)[/tex]:
[tex]\[ -64 \times 0.1540625 = -9.86 \][/tex]
### Step 4: Substitute the fraction back into the original expression and simplify.
Now we substitute [tex]\(-9.86\)[/tex] back into the expression.
[tex]\[ 18.35 - (-9.86) - 4.08 \][/tex]
Remember that subtracting a negative is the same as adding:
[tex]\[ 18.35 + 9.86 - 4.08 \][/tex]
### Step 5: Perform the final addition and subtraction.
First, add [tex]\( 18.35 \)[/tex] and [tex]\( 9.86 \)[/tex]:
[tex]\[ 18.35 + 9.86 = 28.21 \][/tex]
Then subtract [tex]\( 4.08 \)[/tex]:
[tex]\[ 28.21 - 4.08 = 24.13 \][/tex]
So the simplified result is:
[tex]\[ 24.13 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{24.13} \][/tex]
Given the options:
A) 21.23
B) 24.13
C) 29.32
D) 31.35
The correct answer is B) 24.13.
