which expression can be simplified as $\frac{1}{n^{18}}$?

* $(n^2)^9$
* $(n^{-9})^{-2}$
* $(n^{-6})^{-3}$
* $(n^{-3})^6$

Question

which expression can be simplified as $\frac{1}{n^{18}}$?

* $(n^2)^9$
* $(n^{-9})^{-2}$
* $(n^{-6})^{-3}$
* $(n^{-3})^6$

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", "Negative Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Negative Exponents" ] } ## Rewrite the target expression using negative exponents $$ \frac{1}{n^{18}} = n^{-18} $$ ## Apply the power of a power rule to each option $$ \begin{aligned} &(n^2)^9 = n^{2 \cdot 9} = n^{18} \ &(n^{-9})^{-2} = n^{-9 \cdot (-2)} = n^{18} \ &(n^{-6})^{-3} = n^{-6 \cdot (-3)} = n^{18} \ &(n^{-3})^6 = n^{-3 \cdot 6} = n^{-18} \end{aligned} $$ ## Identify the matching expression $$ (n^{-3})^6 = n^{-18} = \frac{1}{n^{18}} $$

(A) $(n^2)^9$

(B) $(n^{-9})^{-2}$

(C) $(n^{-6})^{-3}$

(D) $(n^{-3})^6$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rewrite the target expression using negative exponents

Apply the power of a power rule to each option

Identify the matching expression

Answer: