Question

multiply.

\\7x^4 v^7 \cdot 3v^2 \cdot 2x\\

simplify your answer as much as possible.

Explanation:

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"Multiplying Monomials"
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</pre_analysis>

<reasoning>

Group coefficients and variables

\[
(7 \cdot 3 \cdot 2) \cdot (x^4 \cdot x) \cdot (v^7 \cdot v^2)
\]

Simplify each grouped part

\[

$$\begin{aligned} 7 \cdot 3 \cdot 2 &= 42 \\ x^4 \cdot x^1 &= x^{4+1} = x^5 \\ v^7 \cdot v^2 &= v^{7+2} = v^9 \end{aligned}$$

\]

Combine the simplified parts

\[
42x^5v^9
\]
</reasoning>

<answer>
Multiply.

\(7x^4v^7 \cdot 3v^2 \cdot 2x\)

Simplify your answer as much as possible.

<blank>\(42x^5v^9\)</blank>
</answer>

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

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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],
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"concepts_used": [
"Exponent Rules",
"Multiplying Monomials"
],
"new_concepts": [],
"current_concepts": [
"Exponent Rules",
"Multiplying Monomials"
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}
</pre_analysis>

<reasoning>

Group coefficients and variables

\[
(7 \cdot 3 \cdot 2) \cdot (x^4 \cdot x) \cdot (v^7 \cdot v^2)
\]

Simplify each grouped part

\[

$$\begin{aligned} 7 \cdot 3 \cdot 2 &= 42 \\ x^4 \cdot x^1 &= x^{4+1} = x^5 \\ v^7 \cdot v^2 &= v^{7+2} = v^9 \end{aligned}$$

\]

Combine the simplified parts

\[
42x^5v^9
\]
</reasoning>

<answer>
Multiply.

\(7x^4v^7 \cdot 3v^2 \cdot 2x\)

Simplify your answer as much as possible.

<blank>\(42x^5v^9\)</blank>
</answer>

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