# How do you write (4x^(1/3)y^(5/3))/(16x^(4/3)y^(2/3)) in radical form?

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Evan Share
Apr 28, 2018

#### Answer:

$\frac{y}{4 x}$

#### Explanation:

$\frac{4 {x}^{\frac{1}{3}} {y}^{\frac{5}{3}}}{16 {x}^{\frac{4}{3}} {y}^{\frac{2}{3}}}$

Separate the fraction into like-terms,

$\frac{4}{16} \cdot \frac{{x}^{\frac{1}{3}}}{{x}^{\frac{4}{3}}} \cdot \frac{{y}^{\frac{5}{3}}}{{y}^{\frac{2}{3}}}$

Apply division rule,

$\frac{1}{4} \cdot {x}^{\frac{1}{3} - \frac{4}{3}} \cdot {y}^{\frac{5}{3} - \frac{2}{3}}$

Simplify,

$\frac{1}{4} \cdot {x}^{-} 1 \cdot y$

Combine,

$\frac{y}{4 x}$

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