Sure, let's solve the given expression step by step:
[tex]\[
\frac{\mid 15-(|-6+2|+\sqrt{9})]^2}{3-3^3}
\][/tex]
### Step 1: Calculate the inner absolute value
First, we need to evaluate the expression inside the absolute value:
[tex]\[
|-6 + 2|
\][/tex]
[tex]\[
-6 + 2 = -4 \quad \text{then we take the absolute value:} \quad |-4| = 4
\][/tex]
### Step 2: Calculate the square root
Next, calculate the square root:
[tex]\[
\sqrt{9} = 3
\][/tex]
### Step 3: Add the results
Now, add the results from Step 1 and Step 2:
[tex]\[
4 + 3 = 7
\][/tex]
### Step 4: Subtract this sum from 15 and take the outer absolute value
Now we subtract this sum from 15 and then take the absolute value:
[tex]\[
15 - 7 = 8 \quad \text{thus} \quad |8| = 8
\][/tex]
### Step 5: Square the result
Square the result from Step 4:
[tex]\[
8^2 = 64
\][/tex]
### Step 6: Calculate the denominator
Now, find the value of the denominator:
[tex]\[
3 - 3^3
\][/tex]
First, compute the power:
[tex]\[
3^3 = 27
\][/tex]
Then subtract:
[tex]\[
3 - 27 = -24
\][/tex]
### Step 7: Final division
Finally, divide the squared value by the denominator:
[tex]\[
\frac{64}{-24} = -\frac{64}{24} = -2.6666666666666665
\][/tex]
So, the solution to the given expression is:
[tex]\[
-2.6666666666666665
\][/tex]
