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?
10

rewrite $\sqrt5{4} \cdot \sqrt{2}$ as a single radical.
$\sqrt10{2^3}$
$\sqrt10{2^9}$
$\sqrt9{2^{10}}$

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?
10

rewrite $\sqrt5{4} \cdot \sqrt{2}$ as a single radical.
$\sqrt10{2^3}$
$\sqrt10{2^9}$
$\sqrt9{2^{10}}$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Rational Exponents", "Radical to Exponential Form", "Least Common Denominator" ], "new_concepts": [ "Simplifying Radical Products" ], "current_concepts": [ "Rational Exponents", "Radical to Exponential Form", "Least Common Denominator", "Simplifying Radical Products" ] } ## Convert to rational exponents Using the *Radical to Exponential Form* and *Rational Exponents* knowledge points $$ \begin{aligned} \sqrt[5]{4} \cdot \sqrt{2} &= \sqrt[5]{2^2} \cdot 2^{\frac{1}{2}} \ &= 2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}} \end{aligned} $$ ## Find the least common denominator Using the *Least Common Denominator* knowledge point $$ \begin{aligned} &\text{Denominators: } 5, 2 \ &\text{LCD}(5, 2) = 10 \end{aligned} $$ ## Rewrite with common denominators Using the *Rational Exponents* knowledge point $$ \begin{aligned} 2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}} &= 2^{\frac{4}{10}} \cdot 2^{\frac{5}{10}} \end{aligned} $$ ## Simplify to a single radical Using the *Exponent Rules* and *Radical to Exponential Form* knowledge points $$ \begin{aligned} 2^{\frac{4}{10}} \cdot 2^{\frac{5}{10}} &= 2^{\frac{4}{10} + \frac{5}{10}} \ &= 2^{\frac{9}{10}} \ &= \sqrt[10]{2^9} \end{aligned} $$ ## Question 1 $2^{\frac{2}{5}} \cdot 2^{\frac{1}{2}}$

$4^5 \cdot 2^2$

$4^{\frac{1}{5}} \cdot 2^{\frac{1}{1}}$ ## Question 2 The least common denominator of the exponents is 10. ## Question 3 $\sqrt[10]{2^3}$

$\sqrt[10]{2^9}$

$\sqrt[9]{2^{10}}$

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Rational Exponents" ] }

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QUESTION IMAGE

Question

Explanation:

Convert to rational exponents

Find the least common denominator

Rewrite with common denominators

Simplify to a single radical

Answer:

Question 1

Question 2

Question 3