question 10

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

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

Question

question 10

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

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

Accepted Answer

{ "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" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the exponents of each term

Apply the product rule for exponents

Simplify using negative exponent rule

Answer: