which expression is equivalent to $\frac{\sqrt{2}}{\sqrt3{2}}$?

$\circ$ $\frac{1}{4}$

$\circ$ $\sqrt6{2}$

$\circ$ $\sqrt{2}$

$\circ$ $\frac{\sqrt{2}}{2}$

Question

which expression is equivalent to $\frac{\sqrt{2}}{\sqrt3{2}}$?

$\circ$ $\frac{1}{4}$

$\circ$ $\sqrt6{2}$

$\circ$ $\sqrt{2}$

$\circ$ $\frac{\sqrt{2}}{2}$

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": [ "Rational Exponents", "Radical to Exponential Form", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Rational Exponents", "Radical to Exponential Form", "Exponent Rules", "Simplifying Radical Quotients" ] } ## Convert radicals to exponential form Using the *Radical to Exponential Form* and *Rational Exponents* knowledge points $$ \begin{aligned} \sqrt{2} &= 2^{1/2} \ \sqrt[3]{2} &= 2^{1/3} \end{aligned} $$ ## Apply exponent rules to simplify the quotient Using the *Exponent Rules* knowledge point $$ \begin{aligned} \frac{2^{1/2}}{2^{1/3}} &= 2^{1/2 - 1/3} \ &= 2^{3/6 - 2/6} \ &= 2^{1/6} \end{aligned} $$ ## Convert back to radical form Using the *Radical to Exponential Form* knowledge point $$ 2^{1/6} = \sqrt[6]{2} $$

(A) $\frac{1}{4}$

(B) $\sqrt[6]{2}$

(C) $\sqrt{2}$

(D) $\frac{\sqrt{2}}{2}$

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

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QUESTION IMAGE

Question

Explanation:

Convert radicals to exponential form

Apply exponent rules to simplify the quotient

Convert back to radical form

Answer: