which is the simplified form of the expression \frac{(6^{-4})^{-9}}{6^6}?

\circ \frac{1}{6^{42}}
\circ \frac{1}{6^{19}}
\circ 6^6
\circ 6^{30}

Question

which is the simplified form of the expression \frac{(6^{-4})^{-9}}{6^6}?

\circ \frac{1}{6^{42}}
\circ \frac{1}{6^{19}}
\circ 6^6
\circ 6^{30}

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", "Power of a Power Rule", "Quotient of Powers Rule" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Power of a Power Rule", "Quotient of Powers Rule" ] } ## Simplify the numerator using the Power of a Power Rule $$ (6^{-4})^{-9} = 6^{-4 \times (-9)} = 6^{36} $$ ## Simplify the fraction using the Quotient of Powers Rule $$ \frac{6^{36}}{6^6} = 6^{36 - 6} = 6^{30} $$

(A) $\frac{1}{6^{42}}$

(B) $\frac{1}{6^{19}}$

(C) $6^6$

(D) $6^{30}$

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

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QUESTION IMAGE

Question

Explanation:

Simplify the numerator using the Power of a Power Rule

Simplify the fraction using the Quotient of Powers Rule

Answer: