To evaluate the expression \( \frac{m - n + p}{m^2} \) for \( m = -2 \), \( n = 10 \), and \( p = -20 \), we will follow these steps:
- Calculate \( m - n + p \).
- Calculate \( m^2 \).
- Substitute the values into the expression.
Step 1: Calculate \( m - n + p \)
\[ m - n + p = -2 - 10 - 20 \]
Calculating this step by step:
\[ -2 - 10 = -12 \] \[ -12 - 20 = -32 \]
So, \( m - n + p = -32 \).
Step 2: Calculate \( m^2 \)
\[ m^2 = (-2)^2 = 4 \]
Step 3: Substitute these values into the expression
Now we can substitute \( m - n + p \) and \( m^2 \) into the expression:
\[ \frac{m - n + p}{m^2} = \frac{-32}{4} \]
Now perform the division:
\[ \frac{-32}{4} = -8 \]
Thus, the simplified result of the expression is:
\[ \boxed{-8} \]