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Consider the following expression: 4+(−6)⋅2−(−3)2 . What is the simplified denominator?

5 answers

To simplify the expression \( 4 + (-6) \cdot 2 - (-3)^2 \), let's break it down step by step:

  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. Combine the terms: \( 4 + (-12) = 4 - 12 = -8 \). Now adding \(-9\) to \(-8\): \[ -8 - 9 = -17 \]

So, the entire expression simplifies to: \[ -17 \]

Since the final simplified expression is a single value and not a fraction, there is no denominator involved. If you are looking for a traditional denominator in a fraction format, it would be 1 (since every integer can be expressed over 1).

Thus, the answer is: \[ \text{The simplified denominator is } 1. \]

It's not 1

I apologize for any confusion. Let's clarify the context of "simplified denominator." In the expression you provided, \( 4 + (-6) \cdot 2 - (-3)^2 \), there isn't an explicit denominator since the expression evaluates to a single value.

However, upon reviewing the expression:

\[ 4 + (-6) \cdot 2 - (-3)^2 \]

Here's the correct breakdown of the expression:

  1. Calculate \((-6) \cdot 2\): \[ (-6) \cdot 2 = -12 \]

  2. Calculate \((-3)^2\): \[ (-3)^2 = 9 \]

  3. Substitute the values back into the expression: \[ 4 + (-12) - 9 \]

  4. Combine the terms: \[ 4 - 12 - 9 \] Calculate \(4 - 12\): \[ 4 - 12 = -8 \] Now subtract \(9\): \[ -8 - 9 = -17 \]

Thus, the expression simplifies to \(-17\).

If you are referring to a fraction or a context where there would be a denominator based on this expression, please clarify further so I can address the exact requirement or context you have in mind. If you mean that the expression has specific factors or parts related to a denominator, please provide additional information!

The answer was -9

I apologize for the confusion earlier. Let’s carefully break down the expression step by step to clarify the computation and arrive at the correct interpretation.

The expression we are working with is:

\[ 4 + (-6) \cdot 2 - (-3)^2 \]

Let's simplify it step-by-step correctly:

  1. Calculate \( (-6) \cdot 2 \): \[ (-6) \cdot 2 = -12 \]

  2. Calculate \( (-3)^2 \): \[ (-3)^2 = 9 \]

Now substitute these values back into the expression:

\[ 4 + (-12) - 9 \]

This can be rewritten as:

\[ 4 - 12 - 9 \]

Now combine the terms step by step:

  1. Calculate \( 4 - 12 \): \[ 4 - 12 = -8 \]

  2. Now subtract \( 9 \): \[ -8 - 9 = -17 \]

Thus, the expression evaluates to:

\[ -17 \]

If you meant a specific part of the expression represented as a denominator or if there was a misunderstanding regarding the expression itself, please provide further details.

However, if you are referencing that the value to focus on or a part of your considerations leads to -9 or if you meant a different context entirely, please clarify that scenario so I can assist you accurately.

If I missed any part of your question specifically relating to a denominator, please let me know! Thank you for your patience!