which expression is equivalent to $ \left(\frac{x^{-6}}{x^2}\
ight)^3 $?

* $ \frac{1}{x} $
* $ \frac{1}{x^5} $
* $ \frac{1}{x^9} $
* $ \frac{1}{x^{24}} $

Question

which expression is equivalent to $ \left(\frac{x^{-6}}{x^2}\
ight)^3 $?

* $ \frac{1}{x} $
* $ \frac{1}{x^5} $
* $ \frac{1}{x^9} $
* $ \frac{1}{x^{24}} $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Quotient Rule for Exponents", "Negative Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Quotient Rule for Exponents", "Negative Exponents" ] } ## Simplify the inner fraction $$ \frac{x^{-6}}{x^2} = x^{-6 - 2} = x^{-8} $$ ## Apply the outer exponent $$ (x^{-8})^3 = x^{-8 \cdot 3} = x^{-24} $$ ## Convert to positive exponent $$ x^{-24} = \frac{1}{x^{24}} $$

(A) $\frac{1}{x}$

(B) $\frac{1}{x^5}$

(C) $\frac{1}{x^9}$

(D) $\frac{1}{x^{24}}$

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

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QUESTION IMAGE

Question

Explanation:

Simplify the inner fraction

Apply the outer exponent

Convert to positive exponent

Answer: