Sure, let's break down the expression step-by-step.
Given the expression:
[tex]\[ 8 - \left( (12 - 6 \times 8) \times 3 \right) \div 52 \][/tex]
Let's solve it step-by-step by following the order of operations (PEMDAS/BODMAS):
### Step 1: Evaluate the multiplication inside the parentheses.
Inside the parentheses, you have [tex]\( 6 \times 8 \)[/tex]:
[tex]\[ 6 \times 8 = 48 \][/tex]
### Step 2: Substitute the result back into the expression inside the parentheses.
Now the expression inside the parentheses becomes:
[tex]\[ 12 - 48 \][/tex]
### Step 3: Evaluate the subtraction inside the parentheses.
[tex]\[ 12 - 48 = -36 \][/tex]
### Step 4: Substitute the result back into the main expression.
The main expression now looks like:
[tex]\[ 8 - \left( -36 \times 3 \right) \div 52 \][/tex]
### Step 5: Evaluate the multiplication inside the parentheses.
[tex]\[ -36 \times 3 = -108 \][/tex]
### Step 6: Substitute the result back into the main expression.
The main expression now looks like:
[tex]\[ 8 - (-108) \div 52 \][/tex]
### Step 7: Evaluate the division.
[tex]\[ -108 \div 52 \approx -2.076923076923077 \][/tex]
### Step 8: Substitute the division result back into the main expression.
The main expression now looks like:
[tex]\[ 8 - (-2.076923076923077) \][/tex]
### Step 9: Evaluate the subtraction.
Subtracting a negative is the same as adding the absolute value:
[tex]\[ 8 + 2.076923076923077 \approx 10.076923076923077 \][/tex]
Therefore, the final result of the expression is:
[tex]\[ 10.076923076923077 \][/tex]
