complete the steps to simplify $\sqrt3{4} \cdot \sqrt{2}$.
rewrite using rational exponents.
$2^{\frac{2}{3}} \cdot 2^{\frac{1}{2}}$
$4^3 \cdot 2^2$
$4^{\frac{1}{3}} \cdot 2^{\frac{1}{2}}$

what is the least common denominator of the exponents?

Question

complete the steps to simplify $\sqrt3{4} \cdot \sqrt{2}$.
rewrite using rational exponents.
$2^{\frac{2}{3}} \cdot 2^{\frac{1}{2}}$
$4^3 \cdot 2^2$
$4^{\frac{1}{3}} \cdot 2^{\frac{1}{2}}$

what is the least common denominator of the exponents?

Accepted Answer

{ "quality": "clear", "question_count": 2, "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", "Least Common Denominator" ], "new_concepts": [], "current_concepts": [ "Rational Exponents", "Radical to Exponential Form", "Least Common Denominator" ] } ## Convert radicals to rational exponents Using the *Radical to Exponential Form* and *Rational Exponents* knowledge points $$ \begin{aligned} &\sqrt[3]{4} = 4^{\frac{1}{3}} = (2^2)^{\frac{1}{3}} = 2^{\frac{2}{3}}\ &\sqrt{2} = 2^{\frac{1}{2}}\ &\sqrt[3]{4} \cdot \sqrt{2} = 2^{\frac{2}{3}} \cdot 2^{\frac{1}{2}} \end{aligned} $$ ## Find the least common denominator Using the *Least Common Denominator* knowledge point $$ \begin{aligned} &\text{Exponents: } \frac{2}{3} \text{ and } \frac{1}{2}\ &\text{Denominators: } 3 \text{ and } 2\ &\text{LCD}(3, 2) = 6 \end{aligned} $$ ## Question 1 (A) $2^{\frac{2}{3}} \cdot 2^{\frac{1}{2}}$

(B) $4^6 \cdot 2^2$

(C) $4^{\frac{1}{3}} \cdot 2^{\frac{1}{2}}$ ## Question 2 The least common denominator of the exponents is 6. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Rational Exponents" ] }

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QUESTION IMAGE

Question

Explanation:

Convert radicals to rational exponents

Find the least common denominator

Answer:

Question 1

Question 2