which expression is equivalent to $\left( \frac{125^2}{125^{\frac{4}{3}}} \
ight)$?

* $\frac{1}{25}$
* $\frac{1}{10}$
* 10
* 25

Question

which expression is equivalent to $\left( \frac{125^2}{125^{\frac{4}{3}}} \
ight)$?

* $\frac{1}{25}$
* $\frac{1}{10}$
* 10
* 25

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Rational Exponents" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Rational Exponents" ] } ## Simplify the inner fraction Using the **Exponent Rules** and **Rational Exponents** knowledge points $$ \frac{125^2}{125^{\frac{4}{3}}} = 125^{2 - \frac{4}{3}} = 125^{\frac{6}{3} - \frac{4}{3}} = 125^{\frac{2}{3}} $$ ## Evaluate the simplified expression Using the **Rational Exponents** knowledge point $$ 125^{\frac{2}{3}} = (125^{\frac{1}{3}})^2 = (5)^2 = 25 $$

(A) $\frac{1}{25}$

(B) $\frac{1}{10}$

(C) $10$

(D) $25$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rational Exponents" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the inner fraction

Evaluate the simplified expression

Answer: