Question

when \\(6a^2b^3 \cdot -3a^8b^3\\) is multiplied, the product of the coefficients is dropdown.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Monomial Multiplication",
"Identifying Coefficients"
],
"current_concepts": [
"Monomial Multiplication",
"Identifying Coefficients"
]
}
</pre_analysis>

<reasoning>

Identify the coefficients of each term

The given expression is \(6a^2b^3 \cdot -3a^4b^3\).
The coefficient of the first term \(6a^2b^3\) is \(6\).
The coefficient of the second term \(-3a^4b^3\) is \(-3\).

Multiply the coefficients

\[
6 \cdot (-3) = -18
\]
</reasoning>

<answer>
When \(6a^2b^3 \cdot -3a^4b^3\) is multiplied, the product of the coefficients is <blank>-18</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Monomial Multiplication"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Monomial Multiplication",
"Identifying Coefficients"
],
"current_concepts": [
"Monomial Multiplication",
"Identifying Coefficients"
]
}
</pre_analysis>

<reasoning>

Identify the coefficients of each term

The given expression is \(6a^2b^3 \cdot -3a^4b^3\).
The coefficient of the first term \(6a^2b^3\) is \(6\).
The coefficient of the second term \(-3a^4b^3\) is \(-3\).

Multiply the coefficients

\[
6 \cdot (-3) = -18
\]
</reasoning>

<answer>
When \(6a^2b^3 \cdot -3a^4b^3\) is multiplied, the product of the coefficients is <blank>-18</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Monomial Multiplication"
]
}
</post_analysis>