Answer :

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]