To simplify the expression \( 4 + (-6) \cdot 2 - (-3)^2 \), we'll follow the order of operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
1. Calculate \( (-6) \cdot 2 \):
\[
(-6) \cdot 2 = -12
\]
2. Calculate \( (-3)^2 \):
\[
(-3)^2 = 9
\]
3. Substitute these values back into the expression:
\[
4 + (-12) - 9
\]
4. Now, simplify from left to right:
\[
4 - 12 = -8
\]
\[
-8 - 9 = -17
\]
So, the simplified expression is \(-17\). If you are referring to the denominator of the expression, there is no explicit denominator since this is not a fraction. Thus, the expression itself evaluates to \(-17\). If you are looking for a specific context about a fraction, please clarify.
However, if taken as just a whole number, the "denominator" could be considered as 1 since every integer can be expressed as a fraction over 1. Therefore, one could say the denominator is \(1\).