Question

multiply.

\\2u \cdot 2u^8 v^7 \cdot 6v^3\\

simplify your answer as much as possible.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Exponent Rules",
"Multiplying Monomials"
],
"new_concepts": [],
"current_concepts": [
"Exponent Rules",
"Multiplying Monomials"
]
}
</pre_analysis>

<reasoning>

Group coefficients and variables

\[
(2 \cdot 2 \cdot 6) \cdot (u^1 \cdot u^8) \cdot (v^7 \cdot v^3)
\]

Multiply coefficients and apply exponent rules

\[

$$\begin{aligned} 2 \cdot 2 \cdot 6 &= 24 \\ u^1 \cdot u^8 &= u^{1+8} = u^9 \\ v^7 \cdot v^3 &= v^{7+3} = v^{10} \end{aligned}$$

\]

Combine terms into final monomial

\[
24u^9v^{10}
\]
</reasoning>

<answer>
Multiply.
\[2u \cdot 2u^8 v^7 \cdot 6v^3\]
Simplify your answer as much as possible.
<blank>\(24u^9v^{10}\)</blank>
</answer>

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

<reasoning>

Group coefficients and variables

\[
(2 \cdot 2 \cdot 6) \cdot (u^1 \cdot u^8) \cdot (v^7 \cdot v^3)
\]

Multiply coefficients and apply exponent rules

\[

$$\begin{aligned} 2 \cdot 2 \cdot 6 &= 24 \\ u^1 \cdot u^8 &= u^{1+8} = u^9 \\ v^7 \cdot v^3 &= v^{7+3} = v^{10} \end{aligned}$$

\]

Combine terms into final monomial

\[
24u^9v^{10}
\]
</reasoning>

<answer>
Multiply.
\[2u \cdot 2u^8 v^7 \cdot 6v^3\]
Simplify your answer as much as possible.
<blank>\(24u^9v^{10}\)</blank>
</answer>

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