complete the steps to simplify $\sqrt5{4} \cdot \sqrt{2}$.
rewrite using rational exponents.

$2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$

$4^{5} \cdot 2^{2}$

$4^{\frac{1}{5}} \cdot 2^{\frac{1}{1}}$

Question

complete the steps to simplify $\sqrt5{4} \cdot \sqrt{2}$.
rewrite using rational exponents.

$2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$

$4^{5} \cdot 2^{2}$

$4^{\frac{1}{5}} \cdot 2^{\frac{1}{1}}$

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" ], "new_concepts": [], "current_concepts": [ "Rational Exponents", "Radical to Exponential Form" ] } ## Convert radicals to rational exponents Using the *Radical to Exponential Form* knowledge point $$ \begin{aligned} \sqrt[5]{4} &= 4^{\frac{1}{5}} \ \sqrt{2} &= 2^{\frac{1}{2}} \end{aligned} $$ ## Express with a common base Using the *Rational Exponents* knowledge point $$ \begin{aligned} 4^{\frac{1}{5}} \cdot 2^{\frac{1}{2}} &= (2^2)^{\frac{1}{5}} \cdot 2^{\frac{1}{2}} \ &= 2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}} \end{aligned} $$

(A) $2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$

(B) $4^5 \cdot 2^2$

(C) $4^{\frac{1}{5}} \cdot 2^1$

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

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QUESTION IMAGE

Question

Explanation:

Convert radicals to rational exponents

Express with a common base

Answer: