question 10 multiply: \$a^3 \\cdot a \\cdot a^{-7}\$ * \$a^{11}\$ * \$a^4\$ * \$\\frac{1}{a^3}\$ * \$\\frac{1}{a^4}\$

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponent Rules", "Negative Exponents" ], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Identify the exponents of each term \[ a^3 \cdot a^1 \cdot a^{-7} \] ## Apply the product rule for exponents \[ a^{3 + 1 + (-7)} = a^{-3} \] ## Simplify using negative exponent rule \[ a^{-3} = \frac{1}{a^3} \] (A) $a^{11}$ (B) $a^4$ (C) $\frac{1}{a^3}$ (D) $\frac{1}{a^4}$ { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

question 10 multiply: \$a^3 \\cdot a \\cdot a^{-7}\$ * \$a^{11}\$ *…

QUESTION IMAGE

$question 10 multiply: \$a^3 \\cdot a \\cdot a^{-7}\$ * \$a^{11}\$ *…$

Question

question 10

multiply:
\$a^3 \cdot a \cdot a^{-7}\$

\$a^{11}\$
\$a^4\$
\$\frac{1}{a^3}\$
\$\frac{1}{a^4}\$

Explanation:

Response

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

Identify the exponents of each term

\[
a^3 \cdot a^1 \cdot a^{-7}
\]

Apply the product rule for exponents

\[
a^{3 + 1 + (-7)} = a^{-3}
\]

Simplify using negative exponent rule

\[
a^{-3} = \frac{1}{a^3}
\]
</reasoning>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponent Rules"
]
}
</post_analysis>

Answer: