complete the steps to simplify $\sqrt5{4} \cdot \sqrt{2}$.
rewrite using rational exponents.
$2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$
$4^5 \cdot 2^2$
$4^{\frac{1}{5}} \cdot 2^{\frac{1}{1}}$

what is the least common denominator of the exponents?

Question

complete the steps to simplify $\sqrt5{4} \cdot \sqrt{2}$.
rewrite using rational exponents.
$2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$
$4^5 \cdot 2^2$
$4^{\frac{1}{5}} \cdot 2^{\frac{1}{1}}$

what is the least common denominator of the exponents?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_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 $$ \begin{aligned} \sqrt[5]{4} \cdot \sqrt{2} &= \sqrt[5]{2^2} \cdot 2^{\frac{1}{2}} \ &= 2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}} \end{aligned} $$ ## Identify the exponents Using the *Rational Exponents* knowledge point $$ \text{Exponents: } \frac{2}{5} \text{ and } \frac{1}{2} $$ ## Find the least common denominator Using the *Least Common Denominator* knowledge point $$ \begin{aligned} &\text{Denominators: } 5, 2 \ &\text{LCD}(5, 2) = 10 \end{aligned} $$ What is the least common denominator of the exponents? 10 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Denominator" ] }

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QUESTION IMAGE

Question

Explanation:

Convert radicals to rational exponents

Identify the exponents

Find the least common denominator

Answer: