Certainly! Let's evaluate the expression step by step:
Given expression:
[tex]\[ -0.1 + \frac{12.4}{(-0.2)^2} + 0.01 \][/tex]
### Step 1: Evaluate the exponent
First, we need to evaluate [tex]\((-0.2)^2\)[/tex].
[tex]\[ (-0.2)^2 = (-0.2) \times (-0.2) = 0.04 \][/tex]
### Step 2: Perform the division
Next, we'll divide [tex]\(12.4\)[/tex] by [tex]\(0.04\)[/tex].
[tex]\[ \frac{12.4}{0.04} = 310 \][/tex]
### Step 3: Addition and subtraction with the initial constants
Now we'll put the evaluated division back into the expression:
[tex]\[ -0.1 + 310 + 0.01 \][/tex]
### Step 4: Combine all terms
Add and subtract the terms step by step:
[tex]\[ -0.1 + 0.01 = -0.09 \][/tex]
[tex]\[ -0.09 + 310 = 309.91 \][/tex]
So, the value of the expression is [tex]\(\boxed{309.91}\)[/tex].
