To simplify the expression \( 4 + (-6) \cdot 2 - (-3)^2 \), we should follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
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Compute the exponent: \[ (-3)^2 = 9 \]
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Substitute back into the expression: The expression now becomes: \[ 4 + (-6) \cdot 2 - 9 \]
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Perform the multiplication: \[ (-6) \cdot 2 = -12 \]
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Substitute that value back into the expression: Now, we have: \[ 4 - 12 - 9 \]
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Calculate from left to right:
- First, do \( 4 - 12 \): \[ 4 - 12 = -8 \]
- Now, take that result and subtract 9: \[ -8 - 9 = -17 \]
The simplified expression evaluates to \( -17 \).
Since the question asks for the "simplified denominator," it seems there is some misunderstanding, as there is no denominator in the expression provided. If you meant to refer to the entire expression or its value, the answer is \( -17 \). If you have another expression involving a denominator, please provide that for clarity.
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