which expression is equivalent to $\frac{7^5}{7^2}$?

$\bigcirc$ $(7 \cdot 5) \cdot (7 \cdot 2)$

$\bigcirc$ $(7 \cdot 7 \cdot 7 \cdot 7 \cdot 7) \cdot (7 \cdot 7)$

$\bigcirc$ $\frac{7 \cdot 5}{7 \cdot 2}$

$\bigcirc$ $\frac{7 \cdot 7 \cdot 7 \cdot 7 \cdot 7}{7 \cdot 7}$

Question

which expression is equivalent to $\frac{7^5}{7^2}$?

$\bigcirc$ $(7 \cdot 5) \cdot (7 \cdot 2)$

$\bigcirc$ $(7 \cdot 7 \cdot 7 \cdot 7 \cdot 7) \cdot (7 \cdot 7)$

$\bigcirc$ $\frac{7 \cdot 5}{7 \cdot 2}$

$\bigcirc$ $\frac{7 \cdot 7 \cdot 7 \cdot 7 \cdot 7}{7 \cdot 7}$

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" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Quotient of Powers Rule" ] } ## Expand the numerator and denominator $$ \begin{aligned} 7^5 &= 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \ 7^2 &= 7 \cdot 7 \end{aligned} $$ ## Write the expression as a quotient of expanded factors $$ \frac{7^5}{7^2} = \frac{7 \cdot 7 \cdot 7 \cdot 7 \cdot 7}{7 \cdot 7} $$

(A) $(7 \cdot 5) \cdot (7 \cdot 2)$

(B) $(7 \cdot 7 \cdot 7 \cdot 7 \cdot 7) \cdot (7 \cdot 7)$

(C) $\frac{7 \cdot 5}{7 \cdot 2}$

(D) $\frac{7 \cdot 7 \cdot 7 \cdot 7 \cdot 7}{7 \cdot 7}$

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

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QUESTION IMAGE

Question

Explanation:

Expand the numerator and denominator

Write the expression as a quotient of expanded factors

Answer: